Monday, November 30, 2009


Implications and Relevance of Capital Asset Pricing Model

Capital asset pricing model (CAPM) based on a number of assumptions. Given those assumptions, it provides a logical basis for measuring risk and linking risk and return.
Capital asset pricing model (CAPM) has the following implications,

  • Investors will always combine a risk free asset with a market portfolio of risky assets. They will invest in risky assets in proportion to their market value.
  • Investors will be compensated only for that risk which they cannot diversify. This is the market related systematic risk. Beta which is a ratio of the covariance between the asset returns and the market returns divided by the market variance is the most appropriate measure of an asset’s risk.
  • Investors can expect returns from their investment according to the risk. This implies a liner relationship between the asset’s expected return and its beta.
The concepts of risk and return as developed under capital asset pricing model (CAPM) have intuitive appeal and they are quite simple to understand. Financial managers use these concepts in a number of financial decisions making such as valuation of securities, cost of capital measurement, investment risk analysis excreta. However in spite of its intuitive appeal and simplicity capital asset pricing model (CAPM) suffers from a number of practical problems.
Limitations of Capital asset pricing model
Capital asset pricing model has the following limitations,
  1. It is based on a number of unrealistic assumptions.
  2. It is difficult to test the validity.
  3. Betas do not remain stable over time. (Beta is a measure of a security’s risk).

Sunday, November 29, 2009


Portfolio Theory and Asset Pricing Models

The portfolio is a bundle or a combination of individual asset or securities. The portfolio provides a normative approach to investors to make decisions to invest their wealth in asset or securities under risk. It is based on the assumption that investors are risk averse.

This implies that investors hold well diversified portfolios instead of investing their entire wealth in a single or a few assets.

One important conclusion of the portfolio theory is that if the investors hold a well diversified portfolio of assets, then their concern should be the expected rate of return and risk of the portfolio rather than individual assets and the contribution of individual asset to the portfolio risk.

The second assumption of the portfolio theory is that the returns of the assets are normally distributed. This means that the expected value and variance or standard deviation analysis is the foundation of the portfolio decisions.

Further we can extend the portfolio theory to derive a framework for valuing risky assets. This framework is referred to as the capital asset pricing model (CAPM). An alternative model for the valuation of risky assets is the arbitrage pricing theory (APT).

Friday, November 27, 2009


Normal Distribution and Standard Deviation

The normal distribution is a smooth, symmetric, continuous, bell shaped curve as shown. The distribution is neither skewed nor peaked. The spread of the normal distribution is characterized by the standard deviation.

What is the probability of obtaining a return exceeding or lower than the expected return?
In case of normally distributed returns, it depends only on the standard deviation. It is useful to notice certain properties of a normal distribution.

The distribution tabulated is a normal distribution with mean zero and standard deviation. Such a distribution is known as a standard normal distribution. However any normal distribution can be standardized and hence the table of normal probabilities will serve for any normal distribution.

The formula to standardize is,
S = (R – E (R))/ б
R = Return which we are interested
E (R) = Expected return
Б = Number of standard deviations from the expected return

Thursday, November 26, 2009


Expected Return and Risk

Instead of using historical data for calculating return and risk, we may use forecast ed data. Suppose you are considering buying one share of sunshine industries which has market price of 522.50$ today. The company pays dividend of 5$ per share. You want to hold the share for one year. What is the expected rate of return? This will depend on the dividend on the dividend per share you would actually receive and the market price at which you could sell the share. You do not know both the outcomes. The outcomes may depend on the economic conditions, the performance of the company and other factors. You will have to think of the outcomes of dividend and the share price under possible economic scenarios to arrive at a judgment about the expected return.

Expected Rate of Return

You can put the information summaries the range of returns under the possible states of economic conditions along with probabilities together to calculate the expected rate of return. The expected rate of return is the sum of the product of each outcome and its associated probability.

Risk Preference

The information about the expected return and standard deviation helps an investor to make decision about investments. This depends on the investor’s risk preference. Generally investors would prefer investments with higher rates of return and lower standard deviation. According to the economic principle of diminishing marginal utility, as a person gets more and more wealth his utility for additional wealth increases at a declining rate.

Sunday, November 22, 2009


Historical Capital Market Returns

What rates of returns on shares and other financial instructions have investors earned? You can use indicates for the share prices and other securities for this purpose. We present year by year rates of return for the following financial instruments,
  1. Ordinary shares.
  2. Long term government bonds.
  3. Call money market (This is a portfolio of inter bank transaction).
  4. Treasury bills.
We can summarize the historical capital market returns by two numbers; the average return and the standard deviation. As we have discussed earlier standard deviation summarizes variability and it is a measure of total risk.
Historical risk premium
We can compare the high risk average return on the stock market with the low risk average returns on the government securities. The risk free government security is treasury bills. It is free from risk of default and the variability on its returns is the lowest. This excess return is a compensation for the higher risk of the return on the stock market it is commonly referred to as risk premium.

Tuesday, November 17, 2009


Risk of Rates of Return

The variability of rates of return may be defined as the extent of the deviations or dispersion of individual rates of return from the average rate of return. There are two measures of this dispersion, variance or standard deviation.

The following steps are involved in calculating variance or standard deviation of rates of return of assets or securities using historical returns,

  • Calculate the average rate of return.
  • Calculate the deviation of individual rates of return from the average rate of return and square.
  • Calculate the sum of the square of the deviations as determined in the preceding step and divide it by the number of periods or observations less one to obtain variance.
  • Calculate the square root of the variance to determine the standard deviation.

Monday, November 16, 2009


Risk and Return

Risk and return are most important concepts in finance. In fact, they are the foundation of the modern finance theory.

What is the risk? How is it measured? What is return? How is it measured? How are assets valued in capital markets? How do investors make their investment decisions? We are going to discuss these questions in our future posts.

Return on a single asset

Total return = Dividend + Capital gain

Unrealized capital gain or loss

If an investor holds a share and does not sell it at the end of the period, the difference between the beginning and ending share prices is the unrealized capital gain or loss.
The investor must consider the unrealized capital gain or loss as part of his total return. The fact of the matter is that if the investor so wanted, he could have sold the share and realized the capital gain or loss.

Sunday, November 8, 2009


Equity Capitalization Rate

In our previous posts we discussed how the present value of a share can be calculated, after that we must know how to calculate expected dividends and required rate of return.

The required rate of return will depend upon the risk of the share. Then required rate of return will be equal to the risk free rate of interest plus the risk premium to account for the share’s risk.

In a well functioning capital market, the market price is the fair price of a share. We can use give below equation to estimate the capitalization or the required rate of return of the share,

Ke = (DIV1 / Po) + g

A blind faith in the formula can be misleading. One should be cautious in using the formula.

  • Estimating errors.
  • Unsustainable high current growth.
  • Errors in forecasting dividends.
Linkages between Share price, Earnings and Dividends
Why do investors buy shares? Do they buy them for dividends or for capital gain?
Investors may choose between growth shares or income shares.

  • Growth shares are those, which offer greater opportunities for capital gains.
  • Dividend yield on such shares would generally be low since companies would follow a high retention policy in order to have a high growth rate.
  • Income shares are pay higher rate of dividends, and offer low prospects for capital gains.
Because of the higher payout policy followed by companies their share prices tend to grow at a lower rate.

Monday, November 2, 2009


Valuation of Ordinary Shares

Valuation of ordinary shares is relatively more difficult, because
  1. The rate of dividend on ordinary shares is not known.
  2. The payment of equity dividend is discretionary.
The general principal of valuation applies to the share valuation the value of a share today depends on cash flow expected by investors and risk associated with those cash inflows.
Normally a shareholder does not hold shares in perpetuity. He holds shares for some time, receives the dividends and finally sells them to a buyer to obtain capital gains. When he sells share, a new buyer is also simply purchasing a stream of future dividends and a liquidation price when he also sells the shares.

Single period valuation
Po = (DIV + P1) / (1+ Ke)

Multi Period valuation
Po = {(DIV1 + P1) / (1+ Ke)} + {(DIV 2+ P2) / (1+ Ke)2 }+ ……………….+ {(DIV n+ Pn) / (1+ Ke)n}