Sapm

29-10-2007 SAPM Samuelsons continuous equilibrium theory Economists who have studied the intrinsic value random walk model have accepted and/or modified it in varying degrees. The Nobel Prize winning economist, Paul Samuelson, for eg, has theorized about how security prices would behave if securities mkt where what economists called “perfectly competitive” or “perfectly efficient”. Samuelson supplemented the intrinsic value random walk model describe earlier by defining perfectly efficient prices to be market prices that reflect all information (Paul Samuelson, “ proof that properly discounted present values of assets vibrate randomly”. Bell journal of economics and mgt science, Autumn 1973).

Samuelson suggests that a security with

perfectly efficient prices would be in “continuous equilibrium”. This continuous equilibrium will not be static through time. Every time a new piece of news is released, the securities intrinsic value will change and the securities mkt price will adjust toward the new value. It is the speed of this price adjustment process which gauges the efficiency of a price. A perfectly efficient security price is in a continuous equilibrium such that the intrinsic value of the security vibrates randomly and the mkt price equals the fluctuating intrinsic value at every moment in time. If any disequilibrium (of even a temporary nature) exists, then the securities price is less than perfectly efficient. Of course, actual mkt prices are not perfectly efficient bcoz different security analyst typically assigned different value estimates to any given security.

Actual mkt prices can only peruse a consencus estimate of any given securities intrinsic value since security analysts value estimates differ. If most security analyst value estimate happened to be similar at a point in time, then the consensus value estimate may only vary within a small range. In this case, the seurities price will be almost perfectly efficient as it fluctuates in a narrow range around its changing equilibrium economic value as shown in the figure (a) below,

Price

t

t+n Time Dia.(a) Dia.(b)

30-10-07 Tuesday Both panels (a) & (b) depict two different securities that have the same intrinsic values. Both securities intrinsic values decline immediately at time “t+n”, when some bad news about the security emerges. However, the security in (b) has fallen “indisfavour”. Meaning back few investors are interested in the security. Since very few investors were studying and analyzing the security, large divergences between the securities price and its value could occur. As fig (b) shows the securities price decline more slowly but fluctuated far below its value because not enough investors were continuously estimating the securities value comparing value with price, and making frequent rational buy- sell decisions about it. Fig. (a) Describes an asset that is more efficiently priced than the asset in fig. (b) because, variance (price (a)- value (a))
PASSIVE vs. AGGRESSIVE INVESTMENT MGT. Scientific evidence suggests that expert security analysts can profit from finding under value and overvalue securities. The existence of these lucrative opportunities encourages one to become an aggressive investment manager who buys and sells securities in order to maximize trading profits. AGGRESSIVE INVESTMENT MGT. Securities analysis is at the heart of aggressive investment mgt. it is the present value model which is used in determining the intrinsic value of a share i.e. the discounted value of expected dividends plus the present value of the estimated price of the share in the terminal year. As can be seen, the difficulties (and therefore opportunities in making a trading profit) depend on the accuracy in making these estimates. It requires good education, as well as significant amount of experience, as well as hard work to profit from aggressive investment mgt. PASSIVE INVESTMENT MGT. Because of the scientific evidence suggesting that the prices of securities fluctuate in a random walk that approaches what Samuelson called a continuous equilibrium, passive investment management as become popular since the 1980’s. The passive investors reasoned that if most investors are highly informed and some degree of consensus exists about most securities intrinsic values, then doing securities analysis and trading aggressively is too much trouble and involves too many risks. As a result, many of these

investors invest in special portfolios called Index Funds. Index funds by the same stocks that are in some share mkt index they select. The NSE or the BSE index is a popular index to emulate. The stated investment objective of such an index fund is to perform exactly like the index. Several of these funds manage crores of rupees for passive investments. The efficient mkts research has made such passive investment mgt practices a respectable alternative to estimating values comparing them with prices, and trading aggressively.

DIVWERSIFICATION AND PORTFOIO ANALYSIS Investment are made with the objective of earning some expected rate of return. Investors seek to minimize inefficient deviation from this expected rate of return. Diversification is essential to the creation of an efficient investment because it can reduce the risk (the variability of returns) around the expected return. The portfolio manager seeking efficient investments works with 2 kinds of statistics- expected return statistics and risk statistics. The objective of portfolio analysis is to develop a portfolio that has the maximum return at whatever level of risk the investor deems appropriate. Let us consider some different diversification techniques for reducing a portfolios risk. 1) Simple diversification It can be defined as not putting all the eggs in one basket. Or spreading the risk.

The figure below shows how simple diversification works, the figure was prepared during empirical data on 470 common stocks from the NYSE. The figure shows

FIGURE The level of undiversifiable risk in the market was estimated as.12 (sigma m =.12) 60 different portfolio of each size were assemble from randomly selected stocks to prepare the figure above. Each randomly selected security was allocated and equal weight in its portfolio. From the figure we can see that, on the average, randomly combining 10 to 50 stocks will reduce a portfolios total risk to the undiversifiable level. Spreading the portfolios assets randomly over 2 or 3 times as many stocks cannot be expected to reduce risk any further.