Determinants Of Reutrn

Statistical Measures for Risk

Standard Deviation 1) A measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance.  2) In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility.

  Eg. A volatile stock will have a high standard deviation

while the deviation of a stable blue chip stock will be lower. A large dispersion tells us how much the return on the fund is deviating from the expected normal returns. Standard Deviation Formula for Portfolio Returns

s = Standard Deviation

rk = Specific Return rexpected = Expected Return n = Number of Returns (sample size).

Correlation A measure that determines the degree to which two variable's movements are associated.

The correlation coefficient is calculated as:

The correlation coefficient will vary from -1 to

+1. A -1 indicates perfect negative correlation, and +1 indicates perfect positive correlation

Covariance  A measure of the degree to which returns on two risky assets

move in tandem.  A positive covariance means that asset returns move together.  A negative covariance means returns move inversely.  One method of calculating covariance is by looking at return surprises (deviations from expected return) in each scenario. Another method is to multiply the correlation between the two variables by the standard deviation of each variable.  Possessing financial assets that provide returns and have a high covariance with each other will not provide very much diversification.  For example, if stock A's return is high whenever stock B's return is high and the same can be said for low returns, then these stocks are said to have a positive covariance. If an investor wants a portfolio whose assets have diversified earnings, he or she should pick financial assets that have low

What does required rate of return(RRR) mean?

The rate of return needed to induce investors

or companies to invest in something. Example- For example, if you invest in a stock,

your required return might be 10% per year. Your reasoning is that if you don't receive 10% return, then you'd be better off paying down your outstanding mortgage, on which you are paying 10% interest.

Determinants of Required Returns Three Components of Required Return: The time value of money during the time

period The expected rate of inflation during the period The risk involved

Complications of Estimating Required Return A wide range of rates is available for alternative investments at any time. The rates of return on specific assets change dramatically over time. The difference between the rates available on different assets change over time.

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Determinants of Required Returns The Real Risk Free Rate (RRFR) Assumes no inflation. Assumes no uncertainty about future cash

flows. Influenced by time preference for consumption of income and investment opportunities in the economy

Nominal Risk-Free Rate (NRFR) Conditions in the capital market Expected rate of inflation NRFR=(1+RRFR) x (1+ Rate of Inflation) - 1 RRFR=[(1+NRFR) / (1+ Rate of Inflation)] - 1 8

Determinants of Required Returns Business Risk Uncertainty of income flows caused by the

nature of a firm’s business Sales volatility and operating leverage determine the level of business risk.

Financial Risk Uncertainty caused by the use of debt financing. Borrowing requires fixed payments which must be paid ahead of payments to stockholders. The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium. 9

Determinants of Required Returns Liquidity Risk How long will it take to convert an investment

into cash? How certain is the price that will be received?

Exchange Rate Risk Uncertainty of return is introduced by acquiring securities denominated in a currency different from that of the investor. Changes in exchange rates affect the investors return when converting an investment back into the “home” currency. 10

Determinants of Required Returns Country Risk Political risk is the uncertainty of returns caused

by the possibility of a major change in the political or economic environment in a country. Individuals who invest in countries that have

unstable political-economic systems must include a country risk-premium when determining their required rate of return.

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Determinants of Required Returns Risk Premium and Portfolio Theory From a portfolio theory perspective, the

relevant risk measure for an individual asset is its co-movement with the market portfolio. Systematic risk relates the variance of the

investment to the variance of the market. Beta measures this systematic risk of an asset. According to the portfolio theory, the risk

premium depends on the systematic risk.

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Determinants of Required Returns Fundamental Risk versus Systematic Risk Fundamental risk comprises business risk,

financial risk, liquidity risk, exchange rate risk, and country risk.

Risk Premium= f ( Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk) Systematic risk refers to the portion of an

individual asset’s total variance attributable to the variability of the total market portfolio. Risk Premium= f (Systematic Market Risk) 13

What does risk free return mean? The theoretical rate of return attributed to an

investment with zero risk. The risk-free rate represents the interest on an investor's money that he or she would expect from an absolutely risk-free investment over a specified period of time. In theory, the risk-free rate is the minimum return an investor should expect for any investment, as any amount of risk would not be tolerated unless the expected rate of return was greater than the risk-free rate. In practice, however, the risk-free rate does not technically exist; even the safest investments carry a very small amount of risk. Thus, investors commonly use the interest rate on a three-month U.S. Treasury bill as a proxy for the risk-free rate because short-term government-issued securities

What does risk premium  The return in excess of the risk-free rate of return that mean? an investment is expected to yield. An asset's risk

premium is a form of compensation for investors who tolerate the extra risk - compared to that of a risk-free asset - in a given investment. Think of a risk premium as a form of hazard pay for your investments. Just as employees who work relatively dangerous jobs receive hazard pay as compensation for the risks they undertake, risky investments must provide an investor with the potential for larger returns to warrant the risks of the investment. For example, high-quality corporate bonds issued by established corporations earning large profits have very little risk of default. Therefore, such bonds will pay a lower interest rate (or yield) than bonds issued by lessestablished companies with uncertain profitability and relatively higher default risk.

3 types of Risk Premium a) Equity risk premium- Difference between the return on equity stocks as a class and the riskfree rate represented by the return on treasury Bill. b) Bond Horizon Premium- Difference between the return on long-term government bonds and the return on treasury Bill. c) Bond Default Premium- Difference between the return on long-term corporate bonds and the return on long-term government bonds.