Assignment I Fm.docx

Q. 1

Explain the concept of efficient market hypothesis with example. Explain with examples it three types.

Answer

Define Efficient Market Hypothesis: Efficient market theory means that an investors should earn a return on their investments according to their perceived risk at the time of investment.

Theoretical background Beyond the normal utility maximizing agents, the efficient-market hypothesis requires that agents have rational expectations; that on average the population is correct (even if no one person is) and whenever new relevant information appears, the agents update their expectations appropriately. Note that it is not required that the agents be rational. EMH allows that when faced with new information, some investors may overreact and some may underreact. All that is required by the EMH is that investors' reactions be random and follow a normal distribution pattern so that the net effect on market prices cannot be reliably exploited to make an abnormal profit, especially when considering transaction costs (including commissions and spreads). Thus, any one person can be wrong about the market—indeed, everyone can be—but the market as a whole is always right. There are three common forms in which the efficient-market hypothesis is commonly stated—weak-form efficiency, semi-strong-form efficiency and strong-form efficiency, each of which has different implications for how markets work.

Efficient Market Hypothesis (EMH) The Efficient Market Hypothesis, or EMH, is an investment theory whereby share prices reflect all information and consistent alpha generation is impossible. Theoretically, neither technical nor fundamental analysis can produce risk-adjusted excess returns, or alpha, consistently and only inside information can result in outsized risk-adjusted returns. According to the EMH, stocks always trade at their fair value on stock exchanges, making it impossible for investors to either purchase undervalued stocks or sell stocks for inflated prices. As such, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can possibly obtain higher returns is by purchasing riskier investments.

The Efficient Market Hypothesis Explained Although it is a cornerstone of modern financial theory, the EMH is highly controversial and often disputed. Believers argue it is pointless to search for undervalued stocks or to try to predict trends in the market through either fundamental or technical analysis. While academics point to a large body of evidence in support of EMH, an equal amount of dissension also exists. For example, investors such as Warren Buffett have consistently beaten the market over long periods of time, which by definition is impossible according to the EMH. Detractors of the EMH also point to events such as the 1987 stock market crash, when the Dow Jones Industrial Average (DJIA) fell by over 20 percent in a single day, as evidence that stock prices can seriously deviate from their fair values.

Weak Form Efficient Markets Hypothesis The weak form of the EMH assumes that the prices of securities reflect all available public market information but may not reflect new information that is not yet publicly available. It additionally assumes that past information regarding price, volume, and returns is independent of future prices. It implies that technical trading strategies cannot provide consistent excess returns because past price performance can’t predict future price action that will be based on new information. This form of the EMH, while it discounts technical analysis, leaves open the possibility that superior fundamental analysis may provide a means of outperforming the overall market average return on investment. Example A market is efficient when all information disseminated directly therein is fully reflected in stock prices, thus eliminating the possibility of abnormal profits, i.e. profits generated by investment returns that far exceed the returns of the market. A market is weakly efficient when investors cannot realize abnormal profits by using information such as stock prices and security yields, trading volumes and sales transactions. Ian is a novice investor who has recently developed an interest in investment trading. He is not so experienced, and he wants to collect historical data on the stocks he owns in order to earn an excess return. What should Ian do? Ian observes that the price of a particular stock lost 5% on Monday and earned 3% on Friday. So, Ian decides to purchase 100 shares of this stock for $10 per share. The stock continues to fluctuate, and Ian needs to compare the stock’s current performance with its past performance. Following the technical analysis patterns, he comes to no concrete conclusion. Is the market, perhaps weakly efficient? The answer is yes. The market is weakly efficient because it does not allow Ian to earn an excess return by picking stocks based on their past performance and historical data.

Semi-strong Form Efficient Markets Hypothesis The semi-strong form of the theory dismisses the usefulness of both technical and fundamental analysis. The semi-strong form of the EMH incorporates the weak form assumptions and expands on this by assuming that prices adjust quickly to any new public information that becomes available, therefore rendering fundamental analysis incapable of having any predictive power about future price movements. For example, when the monthly Non-farm Payroll report in the U.S. is released each month, you can see prices rapidly adjusting as the market takes in the new information. Example Agatha buys 500 shares of a construction company that currently trade at $38 per share. A few days later, she reads in the financial news that the company is expected to release outstanding results in the third quarter due to a successful deal with a foreign company. Once the construction company releases its third quarter results, the stock price rises as expected. As a matter of fact, for a week, the stock price rises to $45 but then drops to $36. Agatha wonders why the price does not rise further. Obviously, the market is semi-strong form efficient and adjusts quickly to the newly available information in this case, the company’s strong results. To realize a profit, Agatha should sell some of her shares at $45 per

share as soon as the market adjusted to the new information. Instead, Agatha held all her shares, thus losing money. If Agatha had sold 200 shares at $45 per share, she would realize a gross gain of $9,000. Now that Agatha held all her 500 shares, she loses 500 x $45 – 500 x $36 = $22,500 – $18,000 = $4,500, i.e. the difference between the price she bought the shares and the price they trade. Strong Form Efficient Markets Hypothesis The strong form of the EMH holds that prices always reflect the entirety of both public and private information. This includes all publicly available information, both historical and new, or current, as well as insider information. Even information not publicly available to investors, such as private information known only to a company’s CEO, is assumed to be always already factored into the company’s current stock price. So according the strong form of the EMH, not even insider knowledge can give investors a predictive edge that will enable them to consistently generate returns that outperform the overall market average. Example Most examples of strong form efficiency involve insider information. This is because strong form efficiency is the only part of the efficient market hypothesis that takes into account proprietary information. However, the efficiency theory states that contrary to popular belief, harboring inside information will not help an investor earn high returns in the market. For example, a CTO of a public technology company believes that his company will begin to lose customers and revenues. After the internal rollout of a new product feature to beta testers, the CTO's fears are confirmed, and he knows that the official rollout will be a flop. This would be considered insider information. The CTO decides to take up a short position on his own company, effectively betting against the stock price movement. If the stock price declines, the CTO will profit and, if the stock prices increases, he will lose money. However, when the product feature is released to the public, the stock price is unaffected and does not decline even though customers are disappointed with the product. This market is strong form efficient because even the insider information of the product flop was already priced into the stock. The CTO would lose money in this situation.

Arguments For and Against the Efficient Markets Hypothesis Supporters and opponents of the efficient markets hypothesis can both make a case to support their views. Supporters of the EMH often argue their case based either on the basic logic of the theory, or on a number of studies that have been done that seem to support it. A long-term study by Morningstar found that, over a 10-year span of time, the only types of actively managed funds that were able to outperform index funds even half of the time were U.S. small growth funds and emerging markets funds. Other studies have revealed that less than one in four of even the best-performing active fund managers proves capable of outperforming index funds on a consistent basis. Note that such data calls into question the whole investment advisory business model that has investment companies paying out huge amounts of money to top fund managers, based on the belief that those money managers will be able to generate returns well above the average overall market return.

Opponents of the efficient markets hypothesis tout the simple fact that there ARE traders and investors – people such as John Templeton, Peter Lynch, and Paul Tudor Jones – who DO consistently, year in and year out, generate returns on investment that dwarf the performance of the overall market. According to the EMH, that should be impossible other than by blind luck. But blind luck can’t explain the same people beating the market by a wide margin, over and over again. Over a long span of time. Further, those who argue that the EMH theory is not a valid one point out that there are indeed times when excessive optimism or pessimism in the markets drives prices to trade at excessively high or low prices, clearly showing that securities, in fact, do not always trade at their fair market value. Q. 2 Write a note on liquidity and solvency. Discuss the importance of liquidity and solvency for a bank and manufacturing firm with examples. Answer

Definition: Liquidity refers to the availability of cash or cash equivalents to meet short-term operating needs. In other words, liquidity is the amount of liquid assets that are available to pay expenses and debts as they become due. Obviously, the most liquid asset of all is cash.

What Does Liquidity Mean? Creditors and investors often use liquidity ratios to gauge how well a business is performing. Since creditors are primarily concerned with a company’s ability to repay its debts, they want to see there is enough cash and equivalents available to meet the current portions of debt.

Example Investors, on the other hand, are typically more concerned with the overall health of the business and how it can increase performance in the future. Companies that struggle with liquidity usually have a difficult time growing and increasing performance because short-term funding isn’t available. Poor liquidity is also a sign to investors that the company fails to efficiently generate revenues with its assets to meet its current obligations. Creditors and investors usually prefer higher liquidity levels, but extremely high levels of liquidity could mean the company isn’t properly investing its resources. For example, if cash represents 90 percent of a business’ assets, investors might speculate why these resources aren’t being used to grow the operations and invest in new capital. Creditors obviously won’t care about this much cash because they just want to make sure there is enough money to pay back the loans. Definition: Solvency refers to the long-term financial stability of a company and its ability to cover its longterm obligations. In other words, it’s the ability of a company to meet short and long-term debts as they become due. What Does Solvency Mean? Both investors and creditors are concerned with the solvency of a company. Investors want to make sure the company is in good financial standings and can continue to grow, generate profits, and produce dividends. Basically, investors are concerned with receiving a return on their investment and an insolvent company that has too much debt will not be able to generate these types of returns.

Creditors, on the other hand, are concerned with being repaid. If companies can’t generate enough revenues to cover their current obligations, they probably won’t be able to pay off new obligations. Example Both investors and creditors use solvency ratios to measure a firm’s ability to meet their obligations. The most common solvency ratios are the debt to equity ratio, debt ratio, and equity ratio. The debt to equity ratio compares total liabilities to total equity. This is a comparison of how much money investors have contributed to the company and how much creditors have funded. The more the company owes to creditors, the more insolvent the company is. The debt ratio compares total liabilities to total assets. This shows the amount of assets that are funded by creditors. Conversely, it shows how much assets would need to be sold in order to pay off the liabilities. The equity ratio compares total liabilities to total assets. This shows what percentage of assets investors contribute. Solvency can be viewed in two different ways. Short-term solvency usually focuses on the amount of cash and current assets that can be used to cover obligations. Long-term solvency typically focuses on the firm’s ability to generate future revenues to meet obligations in the future. Liquidity and Solvency of Banks The growth of any economy to a great extent depends largely on the performance of its banking sector. The banking sector works as intermediary linking two parties; who gave the funds and the other party who invested the funds for productive purposes and thereby contributing to economic development. In the financial world, there are two types of banks. One is called commercial banking sector and the other is called Islamic banking sector. The main difference between the two types of bank sectors is the philosophy in which the banking sector depends on. In Islamic banking sector, the interest rate is totally prohibited even it is small or large. Therefore, sometimes, it is called interest-free banking. In the other side, commercial banks are based totally on interest. So, it is called interest-based banks. Nowadays, Islamic banks and commercial banks are working together in a dual regulatory environment and there is a competition between them in attracting potential customers and fulfilling their expectations and developing new instruments and modes of financing which in turn benefits the economy in the long-term. In the United Arab Emirates, the two types of banks are working together in a very competitive environment. Recently, Islamic banks enhance their position in the world and particularly in the UAE during the global financial crisis 2008. Islamic banks are partially affected by the crisis and outperformed than commercial banks (Athanasoglou et al., 2005; Tabash and Dhankar, 2014). Also, from another side, Islamic banks contributed positively to the growth of the economy of UAE (Tabash and Anagreh, 2017). The United Arab Emirates (UAE) gives more attention and support for Islamic banking industry. For example, Dubai Emirate is working on to become a hub for Islamic finance industry in the world. The UAE government supports the Islamic banking industry growth through its strategic plan 2021 (Emirates Diary, 2015). Currently, there are twenty-three local banks and twenty-two international banks working in the UAE. Out of the twenty three local banks, seven are fully-fledged Islamic banks working under Islamic standards as appeared in appendix (1) and the rest banks have both system, Islamic and traditional operations (Emirates Diary, 2015).

Islamic banking sector accounts for 80% of total Islamic finance assets. Organizations like “Ernst & Young, 2015” and the Malaysia Islamic Financial Centre (MIFC) have predicted that the size of the Islamic finance market will reach U.S $3.4 trillion by end of 2018, whilst Price water house Coopers (PwC) predicts a U.S $2.7 trillion market by 2017 (Islamic Finance Report, 2016). In the most of Middle East region countries, the assets of Islamic banking assets are growing faster than commercial banking assets. There are also a huge demand for Islamic banks products from non-Muslim countries like Malaysia, U.K, Germany and Hong Kong (World Bank report, 2015). Liquidity, profitability and solvency are the different dimensions of the performance of any bank. Each of these dimensions is equally important as it plays a vital role in the maintenance of the bank financial viability. If the bank is financially viable it would be able to survive for a long time in the future. The 2008 global financial crisis has made a query on the persistent and increasing fragility of the financial institutions not only in U.S. but also at a global level. Banks have weak capital structure to provide liquidity to interested parties on time. Due to this capital structure, banks are often at the spot in the financial crisis (Diamond and Rajan, 2001). Therefore, the recent global financial crisis has brought to the surface the importance of bank performance and profitability both at national and international level. The banks has an increasing significance in emerging countries because banks are the major source of finance and funding for the majority of firms and are main depository to encourage people for the saving (Athanasoglou et al., 2008). UAE banks are the major financial intermediaries as they are playing a vital role in the economic development of the country. UAE banks have performed well during the recent financial turmoil, as it is evident from its annual credit growth and profitability. In the light of using technology, new generation of both banking types have gained a reasonable position in the banking industry. In this competitive environment, it becomes essential to measure the performance of the banks especially of Islamic banks and commercial banks. So, the main focus of this study is to look into whether the performance of Islamic banks is different from the conventional banks with respect to profitability, liquidity and solvency in UAE and to determine the determinants of profitability for both Islamic and commercial banks. Data and Methodology The present study is analytical in nature and based on secondary data. The data has been collected for Islamic and commercial banks of UAE. Data for Islamic banks is fetched from Islamic Banks and Financial Institutions database (IBIS). The data for commercial banks is fetched from Bank Scope database. The time period of the study includes 4 years ranging from 2011-2014. The sample of the study comprised of 7 fullyfledged Islamic banks and 14 commercial banks of UAE. Different financial ratios have been calculated to measure liquidity, profitability and solvency of UAE Islamic and commercial banks. Independent sample “t” test has been applied to compare the mean of liquidity, profitability and solvency of Islamic and commercial banks of UAE. Microsoft Excel, SPSS 22 and Views 7 are used to do all the tests and statistical analysis. The list of Islamic and commercial banks of UAE is on the appendix 1. Further, in this study, we will check the impact of liquidity and capital adequacy on the profitability of both Islamic and commercial banks in the context of UAE by using stepwise regression model. But before applying the regression analysis, data has been examined against outliers to be valid to the regression model. Therefore, correlation analysis has been done for all variables. As a rule of thumb, if the correlation coefficients between two regressors are less than 0.8, it means there is no multi-collinearity between variables. After correlation test, we can proceed to multiple liner regression models. The current study depends on using stepwise regression model to assess the relationship between ROA, donated as Y and two definite independent variables, denoted as LQ and CA. Researcher found one restriction during the data collection for the mentioned

variables, which is unavailability of data for longer periods particularly for Islamic banks. The regression model for the three variables is written below. Y (ROA)=α+β1 (LQ)+β2 (CA)+?

(1)

Where, ROA: Dependent variable to measure profitability of Islamic and commercial banks. α: constant β1-β2: Coefficients of independent variables. LQ and CA: Independent variables to measure the performance of Islamic and commercial banking sector. Ratios Used • Profitability is a revealing indicator of the efficiency of the bank competitiveness in the market and quality of its management. Return on Assets (ROA) is a barometer of the performance of the bank that measures how efficiently the assets of the banks are being used. Higher the ratio indicates the better profitability of the bank. • Liquidity is crucial for the banks because they are the specialized form of business that is engaged in borrowing and lending. Liquid assets to total assets represent the proportion of assets that bank has in the liquid or cash and cash equivalent. This ratio represents the cash management of the bank (Table 1). • Solvency is related to the ability of the bank to withstand the shocks (Arena, 2005). Capital adequacy ratio is measured to ensure the capacity of the bank in meeting the losses. The higher the ratio, the more will be the protection of investors. Ratios used in this analysis are shown in Table 1. Table 1: Ratios Used 1 Ratio Category Profitability 2 Liquidity 3 Solvency

Ratio Used Return on Assets Liquid Assets to Total Assets Capital Adequacy Ratio

Ahmed et al., 2011 Moore, 2010 Büyük?alvarc? and Abdio?lu (2011)

Results, Analysis and Discussions Liquidity and Solvency Ratios of Islamic Banks It is clear from Table 2 the average ratios for Return on Assets, Liquidity and Capital Adequacy ratios for fully-fledged Islamic banks of UAE over the period 2011-2014. Figure 1 shows the ROA ratio is increasing over time for Islamic banks in the UAE. It gives an indication that Islamic banks are performing well in generating profits of their investments. Figure 2 shows the liquidity ratio for the Islamic banks. We can notice from the figure that the liquidity of Islamic banks is stable over the study period. With respect to capital adequacy ratio, Figure 3 shows that the ratio is also stable for all fully-fledged Islamic banks in the UAE.

Table 2: Ratios For Islamic Banks In UAE Ratios ROA % 2011 1.51 2012 1.23 2013 1.86 2014 2.10

LQ 20.34 23.90 25.47 23.58

CA 14.98 14.02 14.12 14.01

LIQUIDITY AND SOLVENCY OF A MANUFACTURING INDUSTRY Liquidity may be defined as the ability to conform its short - term maturing obligations. The function of liquidity analysis is to quantify a company's ability to meet its short-term debt commitment. Liquidity means conversion of assets into cash during normal courses of business and to have a continuous\ stream of cash to meet outside current debt maturing within one year and also ensure money for day to day operations of business. For a firm that is consistently having difficulty taking on its short-term responsibility is at a higher danger of insolvency. The firm should maintain the adequate cash balance to consider the claims of shortterm creditors, normal operations of business, payment of current interest and dividend requirements. Liquidity comprises of two aspects, time and risk. The time aspect of liquidity refers the speed of conversion of assets in to cash. The risk concern to the degree of certainty about the conversion of inventories, receivable and other assets is into cash with a minimum sacrifice in price. The presentation of financial condition and financial results through financial statement is a meaningless without having adequate cash balance to meet the maturing obligations. The liquidity of a firm varies based on the investment strategy, financial planning goals and risk management. The holding of cash facilitates the benefit of universal acceptance, low risk and the added benefit of almost immediate access in the event of an emergency. A percentage of liquidity reduces the overall risk of portfolio acting as an asset class that holds value. The factors which are affecting on liquidity are the availability of inventory supplies, short term borrowings, and information regarding cash flows, extent of delaying the payment to creditors and offering of cash discounts to customers for encouraging prompt payment. Inadequate liquidity results the loss of some opportunities or some lower purchase prices, deteriorating of the relationship with business partner due to the non-observance of the contracts involved, delays in the payments of the falling due rates and interest related to the loans, difficulties in obtaining of new credits and necessary to sell at a loss a part of the assets in order to be able to pay the current obligations. If a company fails to meet its current obligations, its continued existence is doubtful. The working capital of a business represents the surplus quantity of current assets over current liabilities and it is free to work. It implies that the greater the quantity of working capital, the greater the degree of liquidity of the business. The word liquidity means "the amount of time that is expected to elope until an asset is realized or otherwise converted into cash or until liabilities has been paid", which was used by the financial accounting standard Board (FASB). Liquidity management involves of the amount of investment in the group of assets to satisfy short term maturing obligations. The major part of the fund needed for financing current assets is met from long-term sources and equity, while the balance is obtained from short-term sources. If the maturing commitments are met continuously this will build up the credit worthiness of the firm and the creditors will have confidence in the financial strength of the firm but Failure to meet such responsibilities on a continuous basis will affect the credit report of a firm, which will, in turn, make it more difficult to continue to finance the level of current assets from the short- term sources.

METHODOLOGY OF THE STUDY The data collected from the primary as well as the secondary sources. The secondary data obtained from the annual reports of the Hero Motor Corporation, TVS Motor, Ashok Leyland, Tata Motors, Mahindra & Mahindra, and Maruti Suzuki etc. The data period confined to the 2002-03 to 2014-15 and the SPSS 16.0 version applied to infer the results. The techniques of paired samples statistics, paired samples correlations and paired samples tests were applied to derive the results and conclusions.

That describes the paired samples statistics with the help of various pairs regarding the current ratio. The current ratio of TVS Motor Company was the higher than that of Hero Motors Corporation, and the Ashok Leyland current ratio exceeds the current ratio of Tata Motors Company, but the ratio of Mahindra & Mahindra to Maruti Suzuki lesser than but there was a wider variation between Hero Motor Corporation to the Maruti Suzuki, and Maruti Suzuki ratio exceeds the TVS Motors ratio and the Ashok Leyland possessing more liquidity than the TVS Motor Company and in the same way the liquidity position of the Maruti Suzuki was higher than that of the Hero Motor Corporation. Finally it can be concluded that the higher amount of liquidity possessed by the Maruti Suzuki Company followed by the Ashok Leyland, Mahindra & Mahindra, TVS Motor, Tata Motors and Hero Motor Corporation. The Table.3 describes the relationship between two variables. The pairs Hero Motor Corporation and TVS Motor, Ashok Leyland and Tata Motors and Mahindra & Mahindra with Maruti Suzuki, Maruti Suzuki and Hero Motor Corp, Hero Motor Corp and Maruti Suzuki were the positively correlated but they related with moderate relationship. The remaining pairs namely, TVS Motor and Maruti Suzuki, Ashok Leyland and TVS Motor was negatively correlated and having lesser weak relationship. FINDINGS OF THE STUDY The study pointed out that the following findings. 1. The higher liquidity position (current ratio) possessed by the Maruti Suzuki followed by the Ashok Leyland, Mahindra & Mahindra, TVS Motor, Tata Motors and Hero Motor Corporation. 2. There was positive relationship established regarding Hero Motor Corporation and TVS Motor, Ashok Leyland and Tata Motors and Mahindra & Mahindra to Maruti Suzuki. 3. The study also found that some of the pairs were negatively correlated with TVS Motor and Maruti Suzuki, Ashok Leyland and TVS Motor and the study also identified that there was a significant difference between from one variable to another variable within a pair of all pairs. 4. The study also observed that all the pairs positively correlated except in the two cases TVS Motor and Tata Motors and Ashok Leyland and Hero Motor Corporation. 5. The study also observed that there was a statistically significant difference from the Maruti Suzuki to the Mahindra & Mahindra, Tata Motors to Maruti Suzuki, Maruti Suzuki to Tata Motors and from Ashok Leyland to Hero Motor Corporation, but in a few cases there was no statistically significant difference from the TVS Motor to Tata Motors and TVS Motor and Hero Moto Corp. CONCLUSION AND SUGGESTIONS Finally it can be concluded that there was a statistically significance difference regarding the current ratio and quick ratio which are refers to the liquidity position and also it is suggested that every organization increase in collection of amount from the debtors, do not utilize the working capital funds for purchase of capital goods, establish the planned production schedules to avoid the excessive stocks of finished goods, do not engage in overtrading, manage the cash effectively, reduce the operating cycle, increase the speed of stock turnover by increasing revenue of sales or reducing the level of stocks being carried. The firm can delay in paying its creditors, postponement of some capital expenditure items which are not urgent, chasing up slow paying debtors; generate the reports for internal appraisal of the customer regarding collection of amount. It is also suggested that the organizations should maintain the optimum liquidity position to earn a maximum return; even through the existing liquidity position was satisfactory.

Q.3 Discuss the following: 1. 2. 3. 4. 5. Answer

Time Value of Money Compounding Discounting Annuities Perpetuities

1. The time value of money - The idea that money received in the present is more valuable than the same sum in the future because of its potential to be invested and earn interest -- is one of the founding principles of Western finance. Let's say you lent your friend $2000. Would you rather he repaid you today, or tomorrow? The logical choice would be today, because you'll be able to use your money, and potential gains that come with it, sooner. What Is the Time Value of Money? Money is worth more in the present than in the future because there's an opportunity cost to waiting for it. In addition to your loss of use if you don't get your hands on it right away, there's also inflation gradually eroding its value and purchasing power. If you're going to part with your money for any period of time, you probably expect a larger sum returned to you than you started with. Whether you're lending or investing, the goal is to make a gain to compensate you for going without your money for a while. Suppose your friend offers to repay you $2000 today or $2050 next year. You must consider whether you'd earn more than $50 over the next year by investing your money elsewhere before choosing to delay receiving payment. Other factors include your time preference (whether you need the money right now or can wait awhile to get it back) and whether you trust your friend to actually repay you -- another reason why money is worth more in the present: it may never materialize in the future. As the saying goes, "a bird in the hand is worth two in the bush." Why Does the Time Value of Money Matter? The time value of money matters because, as the basis of Western finance, you will use it in your daily consumer, business and banking decision making. All of these systems are driven by the idea that lenders and investors earn interest paid by borrowers in an effort to maximize the time value of their money. Your job within this system is to limit the cost of money to you and to increase returns on your investments. The concept isn't new -- it dates back to ancient times -- and although, as with Islamic finance, there may be cultures that forbid charging interest, their decisions are driven by similar monetary concepts. Formula for Calculating the Time Value of Money So how do you measure the time value of money? The formula takes the present value, then multiplies it by compound interest for each of the payment periods and factors in the time period over which the payments are made. Formula: FV = PV x [1 + (i / n)] ^ (n x t) (PV) Present Value = what your money is worth right now.

(FV) Future Value = what your money will be worth at some future time after it (hopefully) earns interest. (I) Interest = Paying someone for the time their money is held. (N) Number of Periods = Investment (or loan) period. (T) Number of Years = Amount of time money is held 2.

Compounding

Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods. Compounding, therefore, differs from linear growth, where only the principal earns interest each period. BREAKING DOWN Compounding Compounding typically refers to the increasing value of an asset due to the interest earned on both a principal and accumulated interest. This phenomenon, which is a direct realization of the time value of money (TMV) concept, is also known as compound interest. Compound interest works on both assets and liabilities. While compounding boosts the value of an asset more rapidly, it can also increase the amount of money owed on a loan, as interest accumulates on the unpaid principal and previous interest charges. To illustrate how compounding works, suppose $10,000 is held in an account that pays 5% interest annually. After the first year, or compounding period, the total in the account has risen to $10,500, a simple reflection of $500 in interest being added to the $10,000 principal. In year two, the account realizes 5% growth on both the original principal and the $500 of first-year interest, resulting in a second-year gain of $525 and a balance of $11,025. After 10 years, assuming no withdrawals and a steady 5% interest rate, the account would grow to $16,288.95. Compounding as the Basis of Future Value The formula for the future value (FV) of a current asset relies on the concept of compound interest. It takes into account the present value of an asset, the annual interest rate, and the frequency of compounding (or number of compounding periods) per year and the total number of years. The generalized formula for compound interest is: FV = PV x [1 + (i / n)] (n x t), where: FV = future value PV = present value i = the annual interest rate n = the number of compounding periods per year t = the number of years

3.

Discounting

Present value, also called "discounted value," is the current worth of a future sum of money or stream of cash flow given a specified rate of return. Future cash flows are discounted at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they are earnings or obligations. If you received $10,000 today, the present value would be $10,000 because present value is what your investment gives you if you were to spend it today. If you received $10,000 in a year, the present value of the amount would not be $10,000 because you do not have it in your hand now, in the present. To find the present value of the $10,000 you will receive in the future, you need to pretend that the $10,000 is the total future value of an amount that you invested today. In other words, to find the present value of the future $10,000, we need to find out how much we would have to invest today in order to receive that $10,000 in the future. To calculate present value, or the amount that we would have to invest today, you must subtract the (hypothetical) accumulated interest from the $10,000. To achieve this, we can discount the future payment amount ($10,000) by the interest rate for the period. In essence, all you are doing is rearranging the future value equation above so that you may solve for P. The above future value equation can be rewritten by replacing the P variable with present value (PV) and manipulating the equation as follows:

Let's walk backwards from the $10,000 offered in Option B. Remember, the $10,000 to be received in three years is really the same as the future value of an investment. If today we were at the two-year mark, we would discount the payment back one year. At the two-year mark, the present value of the $10,000 to be received in one year is represented as the following:

Note that if we were at the one-year mark today, the above $9,569.38 would be considered the future value of our investment one year from now. At the end of the first year we would be expecting to receive the payment of $10,000 in two years. At an interest rate of 4.5%, the calculation for the present value of a $10,000 payment expected in two years would be the following:

Of course, because of the rule of exponents, we don't have to calculate the future value of the investment every year counting back from the $10,000 investment at the third year. We could put the equation more

concisely and use the $10,000 as the future value. So, here is how you can calculate today's present value of the $10,000 expected from a three-year investment earning 4.5%:

The present value of a future payment of $10,000 is worth $8,762.97 today if interest rates are 4.5% per year. In other words, choosing Option B is like taking $8,762.97 now and then investing it for three years. The equations above illustrate that Option A is better not only because it offers you money right now but because it offers you $1,237.03 ($10,000 - $8,762.97) more in cash! Furthermore, if you invest the $10,000 that you receive from Option A, your choice gives you a future value that is $1,411.66 ($11,411.66 - $10,000) greater than the future value of Option B. 4.

Annuity

An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees. Annuities are created and sold by financial institutions, which accept and invest funds from individuals and then, upon annuitization, issue a stream of payments at a later point in time. The period of time when an annuity is being funded and before payouts begin is referred to as the accumulation phase. Once payments commence, the contract is in the annuitization phase. Understanding Annuity Annuities were designed to be a reliable means of securing a steady cash flow for an individual during their retirement years and to alleviate fears of longevity risk, or outliving one's assets. Annuities can also be created to turn a substantial lump sum into a steady cash flow, such as for winners of large cash settlements from a lawsuit or from winning the lottery. Defined benefit pensions and Social Security are two examples of lifetime guaranteed annuities that pay retirees a steady cash flow until they pass. Annuity Types Annuities can be structured according to a wide array of details and factors, such as the duration of time that payments from the annuity can be guaranteed to continue. Annuities can be created so that, upon annuitization, payments will continue so long as either the annuitant or their spouse (if survivorship benefit is elected) is alive. Alternatively, annuities can be structured to pay out funds for a fixed amount of time, such as 20 years, regardless of how long the annuitant lives. Annuities can also begin immediately upon deposit of a lump sum, or they can be structured as deferred benefits. An example of this type of annuity is the immediate payment annuity in which payments begin immediately after the payment of a lump sum. Deferred income annuities are the opposite of an immediate annuity because they don't begin paying out after the initial investment. Instead the client specifies an age at which he or she would like to begin receiving payments from the insurance company. Annuities can be structured generally as either fixed or variable. Annuities provide regular periodic payments to the annuitant. Variable annuities allow the owner to receive greater future cash flows if investments of the annuity fund do well and smaller payments if its investments do poorly. This provides for a less stable

cash flow than a fixed annuity, but allows the annuitant to reap the benefits of strong returns from their fund's investments. One criticism of annuities is that they are illiquid. Deposits into annuity contracts are typically locked up for a period of time, known as the surrender period, where the annuitant would incur a penalty if all or part of that money were touched. These surrender periods can last anywhere from two to more than 10 years, depending on the particular product. Surrender fees can start out at 10% or more and the penalty typically declines annually over the surrender period. While variable annuities carry some market risk and the potential to lose principal, riders and features can be added to annuity contracts (usually for some extra cost) which allow them to function as hybrid fixedvariable annuities. Contract owners can benefit from upside portfolio potential while enjoying the protection of a guaranteed lifetime minimum withdrawal benefit if the portfolio drops in value. Other riders may be purchased to add a death benefit to the contract or accelerate payouts if the annuity holder is diagnosed with a terminal illness. Cost of living riders are common to adjust the annual base cash flows for inflation based on changes in the CPI.

Annuities: Who Sells Them Life insurance companies and investment companies are the two sorts of financial institutions offering annuity products. For life insurance companies, annuities are a natural hedge for their insurance products. Life insurance is bought to deal with mortality risk – that is, the risk of dying prematurely. Policyholders pay an annual premium to the insurance company who will pay out a lump sum upon their death. If policyholders die prematurely, the insurer will pay out the death benefit at a net loss to the company. Actuarial science and claims experience allows these insurance companies to price their policies so that on average insurance purchasers will live long enough so that the insurer earns a profit. Annuities, on the other hand, deal with longevity risk, or the risk of outliving ones assets. The risk to the issuer of the annuity is that annuity holders will live outlive their initial investment. Annuity issuers may hedge longevity risk by selling annuities to customers with a higher risk of premature death. In many cases, the cash value inside of permanent life insurance policies can be exchanged via a 1035 exchange for an annuity product without any tax implications. Annuities: Who Buys Them Annuities are appropriate financial products for individuals seeking stable, guaranteed retirement income. Because the lump sum put into the annuity is illiquid and subject to withdrawal penalties, it is not recommended for younger individuals or for those with liquidity needs. Annuity holders cannot outlive their income stream, which hedges longevity risk. So long as the purchaser understands that he or she is trading a liquid lump sum for a guaranteed series of cash flows, the product is appropriate. Some purchasers hope to cash out an annuity in the future at a profit, however this is not the intended use of the product. Immediate annuities are often purchased by people of any age who have received a large lump sum of money and who prefer to exchange it for cash flows in to the future. The lottery winner's curse is the fact that many lottery winners who take the lump sum windfall often spend all of that money in a relatively short period of time.

5.

Perpetuity

Perpetuity is a very important concept in corporate finance. The concept of perpetuity makes it possible to value stocks, real estate and many other investment opportunities. The valuation of perpetuities is theoretically very simple. The concept of perpetuity as well as the formula required for its calculation has been explained in this article: Stream of Cash Flows that Never Terminates In corporate finance, we try to compare the value of different streams of cash flows. Sometimes, we exchange a lump sum value for a finite stream of future payments. However, in case of perpetuity, the payments will never cease. A perpetuity is basically a stream of cash flows that never terminates. This means that if we purchase a perpetuity right now after paying a certain lump sum, we should expect repayments that last till the end of time. Examples of Perpetuities Although, valuing a perpetuity may not seem intuitive in the first place, it is required. There are many forms of investments that mimic the features of a perpetuity. Consider the example of common stocks. Common stocks are basically an investment in the operations of a company. Theoretically the company has an infinite life. Therefore the shareholder is entitled to an infinite stream of future dividends for paying the stock price now. It is for this reason that common stocks are valued as a perpetuity. Many universities have endowment funds that pay scholarships to students. They have been doing so for centuries and plan to continue to do so forever. These funds were invested in a perpetuity by a philanthropist many years ago. Now it continues to make payments till the end of time! Why Perpetuities Have a Finite Value? The most counter-intuitive part of perpetuity is the fact that it has a finite value. The question that comes to everybody’s mind is that how can a series of infinite cash flows have a finite valuation. The answer is because the real value of future cash flows keeps on falling. The present values are high in the early years. However, the payment amount is fixed under a perpetuity. Therefore in the later years as and when inflation keeps on increasing, the real value of the payments are continuously decreasing. It is because of this that the cash flows in the very distant future will have a near zero valuation although it will never exactly be zero. Hence using the formula for sum of an infinite series, the value of a perpetuity can be calculated. Formula for Valuing Perpetuities The formula for valuing perpetuities is very simple and straightforward. It is as follows: PV = C / R Where: PV is the present value of perpetuity C is the amount of cash flow received every period R is the required rate of return

Q. 4 Discuss the following: 1. 2. 3. 4.

Technical Analysis Fundamental Analysis Horizontal Analysis Vertical Analysis

Answer 1.

Technical Analysis

Technical analysis is a methodology that makes buy and sell decisions using market statistics. It primarily involves studying charts showing the trading history and statistics for whatever security is being analyzed. How does Technical Analysis Work To perform technical analysis, investors start with charts that show the price and trading volume history of a particular security or index (for example, the Dow Jones Industrial Average) as well as host of other statistical measures such as moving averages, maximums and minimums, and percentage changes. The idea is to use the charts to identify trends and changes in those trends. There are several kinds of trends and patterns, some with unusual names: rectangles, triangles, Bollinger bands, inverted heads and shoulders, candlesticks, the MACD histogram, stochastic, and so forth. Some technical analysts also use indicators and oscillators to interpret trading data. Why does Technical Analysis matter? Unlike fundamental analysis -- which focuses on finding a security's "true value" by studying financial statements, market outlooks, competition, macroeconomic events, etc. -- technical analysis is based on the belief that past market trends can predict the future behavior for the market as a whole and for individual stocks. If an investor can correctly interpret a chart's "message" and predict a stock's movement, he or she can obviously make a lot of money. Certain aspects of technical analysis are controversial, such as the belief that stocks and markets move in trends that can play out over a long period of time, and the contention that market action can detect shifts in supply/demand relationships. Most investors tend to be either technicians or fundamental investors, though many analysts believe that combining technical and fundamental analysis is the best way to evaluate exit and entry points. Since many people believe in technical trading rules, at the very least the rules can become self-fulfilling, making them important to know for the individual investor. 2.

Fundamental Analysis

Fundamental analysis is a method of evaluating the intrinsic value of an asset and analyzing the factors that could influence its price in the future. This form of analysis is based on external events and influences, as well as financial statements and industry trends. Fundamental analysis is one of two major methods of market analysis, with the other being technical analysis. While technical traders will derive all the information they need to trade from charts, fundamental traders look at factors outside of the price movements of the asset itself.

How does Fundamental Analysis Work Fundamental analysis observes numerous elements that affect stock prices such as sales, price to earnings (P/E) ratio, profits, earnings per share (EPS), as well as macroeconomic and industry specific factors. Fundamental analysts use either top-down or bottom-up methods of analysis, or sometimes both. A top-down analysis might function in the following manner: 1)

The entire market is analyzed, including global and macroeconomic indicators

2)

The specific sector, such as Technology

3)

The industry, for example semiconductor manufacturer

4) The specific stock, for example company ABC Conversely, a bottom-up analysis starts by investigating specific stocks first. The fundamental analyst observes trends, market and price movements, company financial statements, interest rates, return on equity (ROE), and numerous other indicators with one goal in mind: buying or selling stocks that will provide a high return on investment (ROI) KEY TAKEAWAYS     

Fundamental analysis attempts to measure a security's intrinsic value. Fundamental analysis seeks to identify securities that are not correctly priced by the market. Investors can utilize fundamental analysis to optimize their portfolio's performance. If the fair market value is higher than the market price, then the stock is deemed to be undervalued and a buy recommendation is given. Conversely, if the fair market value is lower than the market price, then the stock is considered to be overvalued and a sell recommendation is issued.

Examples of Fundamental Analysis There are various tools and techniques that can be used for fundamental analysis, but they have been categorized into two types of fundamental analysis: top-down analysis and bottom-up analysis. Top-down analysis takes a broader view of the economy, starting with the entire market before narrowing down into a sector, industry and finally a specific company. Conversely, bottom-up analysis starts with a specific stock and widens out to consider all the factors that impact its price. Most fundamental analysis is used for evaluating share prices, but it can be used across a range of asset classes, such as bonds and forex. The tools that traders might choose for their fundamental analysis vary depending which asset is being traded. For example, share traders might choose to look at the figures in a company’s earnings report: revenue, earnings per share (EPS), projected growth or profit margins. While forex traders may choose to assess the figures released by central banks that allow insight into the state of a country’s economy.

3.

Horizontal Analysis

Horizontal analysis of financial statements involves comparison of a financial ratio, a benchmark, or a line item over a number of accounting periods. This method of analysis is also known as trend analysis. Horizontal analysis allows the assessment of relative changes in different items over time. It also indicates the behavior of revenues, expenses, and other line items of financial statements over the course of time. Accounting periods can be two or more than two periods. Accounting period can be a month, a quarter or a year. It will depend on the analyst’s discretion when choosing an appropriate number of accounting periods. During the investment appraisal, the number of accounting periods for analysis is based on the time horizon under consideration. Horizontal analysis of financial statements can be performed on any of the item in the income statement, balance sheet and statement of cash flows. For example, this analysis can be performed on revenues, cost of sales, expenses, assets, cash, equity and liabilities. It can also be performed on ratios such as earnings per share (EPS), price earnings ratio, dividend payout, and other similar ratio. Horizontal analysis can be performed in one of the following two different methods i.e. absolute comparison or percentage comparison.  Absolute Comparison: One way of performing horizontal analysis is comparing the absolute currency amounts of some items over the period of time. For example, cash in hand at the end of an accounting period can be compared to other accounting periods. This method is helpful in identifying the items which are changing the most.  Percentage Comparison: In the second method of horizontal analysis, percentage differences in certain items are compared over a period of time. The absolute currency amounts are converted into the percentages for the purpose of comparison. For example, a change in cash from $5,000 to $5,500 will be reported as 10% increase in cash. It can also be reported as 110%, which means that the cash is 110% of the cash at the end of previous accounting period. This method is useful when comparing performance of two companies of different scale and size. What Does Horizontal Analysis Mean This formula for evaluation is typically done by either investors and internal company management since both need to understand how well a company is doing in order to make decisions. Investors have to make the decision whether or not they want to invest or sell their current investment; while management needs to know what moves to make in order to improve the future performance of the company. Since, any line item in a financial statement or financial ratio can be compared across a period of time, it makes the horizontal analysis extremely useful for anyone trying to track a company’s performance over time. Example An investor can see if a business is expanding and becoming more valuable or becoming less efficient and less valuable. For example, an investor can use the horizontal analysis of the balance sheet to track the earnings per share ratio on a company he is thinking about investing in. If the ratio continues to grow year over year, the investor’s analysis would show a positive trend and he would probably choose to invest in the company granted other metrics are equally as positive.

A manager, on the other hand, is concerned with the day-to-day operations of the company, so he uses this evaluation technique to pinpoint areas for improvement. For instance, a manager might compare cost of goods sold and profit margin over a two or three-year span to see how efficient the company is becoming. This comparison of income statements will give the manager not only a benchmark for future performance; it will also help him understand what needs to be changed in the future. Although this comparison is useful on its own, investors and management typically use both horizontal and vertical analysis techniques before making any decisions.

4.

Vertical Analysis

Vertical analysis is a method of financial statement analysis in which each line item is listed as a percentage of a base figure within the statement. Thus, line items on an income statement can be stated as a percentage of gross sales, while line items on a balance sheet can be stated as a percentage of total assets or liabilities, and vertical analysis of a cash flow statement shows each cash inflow or outflow as a percentage of the total cash inflows. How Vertical Analysis Works Vertical analysis makes it much easier to compare the financial statements of one company with another, and across industries. This is because one can see the relative proportions of account balances. It also makes it easier to compare previous periods for time series analysis, in which quarterly and annual figures are compared over a number of years, in order to gain a picture of whether performance metrics are improving or deteriorating. For example, by showing the various expense line items in the income statement as a percentage of sales, one can see how these are contributing to profit margins and whether profitability is improving over time. It thus becomes easier to compare the profitability of a company with its peers. Example Vertical analysis is said to get its name from the up and down motion of your eyes as you scan the commonsize financial statements during the analysis process. Most often, vertical analysis is used by management to find changes or variations in financial statement items of importance like individual asset accounts or asset groups. Vertical analysis follows the same concept as benchmarking. Management sets a base amount or benchmark goal to judge the success of the business. The base amount is usually taken from an aggregated from the same year’s financial statements. Then the common-size percentage formula can be applied to the financial item. The common-size percentage formula is calculated by dividing the analyzed item by the base amount of benchmark and multiplying it by 100.

This percentage can be used to compare both balance sheet and income statement performance within the company. Much like ratio analysis, vertical analysis allows financial information of a small company to be

compared with that of a large company. The common size percentage can also be used to compare different companies within the same industry or companies that use different currencies.

Q. 5

Explain Modern Portfolio Theory (MPT). Discuss types of risk highlighted by MPT with Example.

Modern Portfolio Theory (MPT) is an investment theory whose purpose is to maximize a portfolio’s expected return by altering and selecting the proportions of the various assets in the portfolio. It explains how to find the best possible diversification. If investors are presented with two portfolios of equal value that offer the same expected return, MPT explains how the investor will prefer and should select the less risky one. Investors assume additional risk only when faced with the prospect of additional return. In brief, MPT explains how investors can reduce overall risk by holding a diversified portfolio of assets. The Best Portfolios Are on the Efficient Frontier With MPT, investors create portfolios to maximize the expected return based on a given level of risk. And, according to the theory, the best way to identify optimal diversification is through something called an efficient frontier. The efficient frontier is made of portfolios that offer the greatest expected returns for a given level of risk… or vice versa, the lowest risk for a given level of expected returns. Markowitz — and a cadre of economists who would fine-tune MPT over the decades — created a set of complicated mathematical formulas. They define the boundaries of the efficient frontier. Luckily, we’re not expecting you to be able to fully master and apply these formulas to your portfolio yourself. That’s because there’s an entire group of services online to help you make the most out of MPT in your own investment portfolio. How You Can Use MPT in Your Portfolio Robo advisors are among the hottest recent trends in the investing world. These services use computer algorithms to create asset allocations in your portfolio. And, for the most part, these algorithms use the principles of Modern Portfolio Theory. In fact, Investor Junkie’s favorite robo advisor, Wealth front, published a white paper outlining its use of MPT, calling it “the best framework on which to build a compelling investment management service.” Meaning of Modern Portfolio Theory (MPT) MPT Postulates those savers are generally risk averse and try to reduce risk by all possible methods. The markets are perfect and absorb all information perfectly and returns are the same whenever you enter the market. The principal of Dominance is applied to select a portfolio as the frontier line. MPT depends on the concepts of diversification and use of Beta for reducing the risk and the concept of Dominance for selection of a Portfolio with least risk, with returns being given. Basis of Modern Portfolio Theory (MPT)

The Tripod on which the MPT depends are diversification of Markowitz type, concept of Dominance and use of Beta. A. Diversification-Investment in more than one security, asset, industry etc. with a view to reduce risks: Diversification — an example: Expected Return of X = 20% Expected Return of Y = 30% Risk (a) of Security X = 10% Risk (a) of Security Y = 16% Coefficient of correlation, between X and Y can have three scenarios -1, 0.5 or + 1. Corresponding graph looks as follows: Investment in X = 40% and in Y = 60%.

Return on Portfolio = 26% = (20 x 0.4 + 30 x 0.6) Risk on Portfolio = 13.6%, which is normal average risk (10 x 0.4 + 16 X 0.6). If diversification has to give an advantage, the coefficient of correlation is to be considered. If the average risk of Portfolio has to be less than 13.6%, the coefficient of correlation of these returns of X and Y has to be less than 1.0. If the coefficient is + 1.0, the return moves along the straight line AB. Suppose it is – 1.0, then the risk can be reduced to zero, because the risk of the one can be perfectly offset by that on the other. If it is 0.5 (or anything between + 1.0 and -1.0) then the diversification can reduce the risk on the Portfolio and the return will move along the curve. This is explained easily by graphical method rather than mathematical method. If you are on the Curve AB rather than straight line AB you can improve return without increasing the risk, at say point Q from Q to P at the same level of risk. B. CAP Theory and Concept of Dominance (Capital Assets Pricing Model): Risk and return have a relationship. If you want to increase the return you should also be prepared to accept higher risk. You are entitled to various combinations of assets in your Portfolio. These combinations are called opportunity set — a set of all possible Portfolios given the constraint of money available for investment.

The upper boundary of the opportunity set is called the efficient frontier because by so moving, you are improving the return for the same level of risk as shown below. You move from Point Q to Point P, both of which are within the opportunity set but by such move you improve the return and this proves to be more efficient. The Portfolio Manager has to do this by constantly analyzing the company’s performance/returns vis-a-vis the risk. Role of Beta: According to CAPM, the market related risk and not total risk is relevant. This systematic risk can be reduced by using Betas. It is a measure of sensitivity of the return of one asset to the market return. Every asset will have a total return comprising two components: (a) Risk free return — a return for mere waiting or loss of liquidity for the period of investment. (b) Risk premium, which is return for risk taking and varies from asset to asset. Modern portfolio theory postulates the following axioms: 1. Diversification reduces the total risk but applicable only to company specific unsystematic risk. 2. CAPM states that where shares are correctly priced every security is expected to earn returns commensurate with the risk it carries. 3. The riskiness of a security is to be seen in the context of Portfolio or market related risk, but not in isolation. 4. The importance of Beta is for managing non-diversifiable part of risk. Risk Management Strategy: Corresponding to two types of risks — diversifiable (unsystematic) and non- diversifiable risks (systematic) the portfolio risk can be managed by: (a) Diversification and management of duration of the Portfolio. This will take care of the diversifiable risk and interest rate risk. (b) Use of Beta for Management of Systematic Risk. Duration:

The concept of duration can be explained by taking the life or maturity period of the asset class. If the bond has zero coupon rate, its duration is the same as its maturity. But the duration of equity is infinity, but represented by or MP/EPS or MP/DPS where EPS is Earnings per Share and DPS is Dividend per Share. The average Market price is I’ and EPS is related to MP by what is called the market P/E Ratio, representing the above equation, the market P/E has its duration as 20-25 at present. The duration of bonds of debentures is the life to maturity and the duration of cash and money market instrument is zero. Theoretical discussion on duration is generally confined to Bond Portfolio Management for which a reference may be made to the author’s book “Security Analysis and Portfolio Management.” Example: The duration can be made about 5 years by adopting the following investment pattern explained in a crude manner: 15% in Equity (25 years) 0.15 x 25 = 3.75 60% in Bonds/Debentures (5 year maturity) 0.6 x 3 =1.8 25% in Money Market Instruments 0.25 x 0 =0 Total Duration = 5.55 Duration means the weighted average measure of time period of bond’s life of any asset or portfolio. Beta: Management of Beta is done as follows: Beta on equity shares varies from company to company. Calculate the Betas and take the average Beta, for selected Scrips in the Portfolio. If investor wants the market risk and market return, then the Beta of the Portfolio should be 1. If the actual shares in the Portfolio give a Beta of 1.2, then an investment of 80% in equities gives the Portfolio Beta as 1.2 x 0.8 = 0.96 and the rest of the 20% is invested in bonds and money market instruments. If the investor is risk taking then the Portfolio should be aggressive with Beta of more than 1. If on the other hand he is risk averse, the Portfolio Beta should be less than 1 and it is a defensive Portfolio. Thus, the investment strategy should be decided after laying down first the allocation of funds to different asset classes in the form of proportions and then the selection of instruments and Scrips would be decided within each asset class, based on their fundamentals.

It will be seen from the Table that Betas vary with the time periods of study; high Betas based on historical data do not reflect the price volatility and there is no-guarantee that high Betas go with high return and low Betas go with low returns. Table 1 presents the data on selected companies with Betas, price volatility (High/ low ratios) Earnings Per Share (EPS) and the Betas for 1999. It is seen from the Table that historical Betas are not correlated with either price volatility or earnings per share, and that Betas change over time. Target Return: The basic principle in the market is that the higher the risk taken, the higher is the return. An investor who wants only risk free return can have all his funds invested in Government bonds and bank deposits which will yield only risk free return of around 10% – 14% and sometimes less. But if the investor wants to have a higher return and takes risk accordingly, then risk premium will be available to him. Assuming the riskless return as 12% if he wants a return of 25%, then the risk premium should be 13%. The portfolio Manager has to invest the majority of his funds in equities with a Beta, of more than 1. If the market return is 20% then with a Beta of 1.3, he will get 26%, which is the target return. Borrowing for Investment: Equities are most risky and have long duration and their Betas are high. Bonds have negligible Beta and moderate duration while Money Market instruments have negligible or zero duration. The range of Beta and duration can be widened by borrowing for investment. If a fund manager with Rs. 1 lakh borrows another Rs. 1 lakh and invests Rs. 2 lakh, in equity Portfolio, even with a Beta of 1.00, his overall Portfolio Beta is actually 2.00 because his Portfolio is Rs. 1 lakh and his equity Portfolio is Rs. 2 lakh (which is 200% of his own Portfolio). This gives almost double the returns expected and even after paying the interest component on borrowed funds, he enjoys the leverage and improves his net worth. This assumes that return on capital employed is more than the cost of borrowing. Mathematical Models of Modern Portfolio Theory:

Graphical Method can explain the portfolio selection in case of two or a few assets. Use of dominance principle asserts that those assets which show higher expected returns for the given level of risk will be selected. Dominant assets are called efficient portfolios whether they contain two or more assets. An efficient portfolio is thus any set or combination of assets that has the maximum expected return in its risk class and/or the minimum risk at the given level of expected return. The objective of Portfolio Theory is to explain the behavior of investor in selection of efficient portfolios. The portfolio expected return is the weighted average of the expected rates of return of the assets in the portfolio. The expected return for a portfolio denoted by E (rp) for “n” asset-portfolio is represented by-

Where x is the fraction of the total value of the portfolio invested in the i th asset. The r’s can be called weights to each of the assets. E (ri) represents the expected rate of return from the i th asset. The sum of the weights is equal to 1, or

If there are ‘n’ number of assets which are considered for investment in the market their risk and return characteristics have to be ranked in the order of highest return to lowest return and in the order of lowest risk to the highest risk. The selection of the assets can be based on some criteria of dominance say maximum expected return for a given level of risk. A computer aided mathematical program can be designed to select the assets in the portfolio, subject to save given constraints, such as a tolerable level of risk, total amount of investible funds or a minimum expected return for a given level of risk. An efficient solution technique for portfolio selection lies in the use of differential calculus or linear programming. A general form of the Model using the mathematical programme is set out below. Calculus can be used to find a minimum risk portfolio for any given expected return E (x). Mathematically the problem involves the finding of the minimum portfolio variance. Thus minimize variance:

Subject to two Lagrangian constraints. Constraint Number 1 is that the desired expected return E® is achieved.

Constraint Number 2 is that the sum of the weights given to assets in the portfolio is unity.

Combining the above three equations yields the Lagrangian objective function of the risk minimization problem with a desired return constraint.

Martin A.D. Jr. solved this problem in the article published by him “Mathematical Programming of Portfolio Selection”, Management Science, January 1955. The minimum risk portfolio is found by setting dz/dxt = 0 for t = 1 … n and dz/dλt = 0 for t = 1, 2 … n and then solving the system of equations for the xt’s. The number of assets analyzed is ‘n’ and can be any positive integer.