Capital Assets Pricing Model (CAPM)

Capital Assets Pricing Model (CAPM)
Markowitz portfolio theory suggests that the investment decision should be based on the total risk and price of assets should be also determined on the basis of total risk. But the CAPM suggests that, any investor can create a portfolio of assets that will eliminate all diversifiable risk (as undiversifiable risk can’t be diversify away .) Therefore the only relevant risk is non-diversifiable risk. Thus the investment decision and the pricing of capital assets should be based on the undiversifiable risk, The relationship between an asset’s return and its systematic risk can be expressed by the CAPM. The CAOM tries to quantify the required rate of return at a given level of systematic risk. In other word CAPM gives idea about, how much return (required rate of return - RRR) should be necessary for given level of systematic risk beta. For this we us following equation.

RRR = Rf + ( Rm – Rf ) . ąβ

Where, RRR = Required rate of return or expected rate of return
Rf = Risk free rate of return
Rm = Market return
B= Beta coefficient
( Rm – Rf ) = Slope of CAPM





CAPM is also known as security Market Line (SML) . SML is the line showing the relationship between the systematic risk index (beta) and the required rate of return.




Arbitrage Pricing Theory (APT)
Chapter 11
APT (Based on ‘ Law of one price’)

Arbitrage opportunity refers to buying of the same securities in the less costlier market and selling it in the expensive market with zero initial cash outlay and zero incremental risk (often known as risk free investment)

Arbitrage is the process of earning risk less profits by taking advantage of differential pricing for the same physical asset or security. As a widely applied investment tactic, arbitrage typically entails the sale of a security at a relatively high price and the simultaneous purchase of the same security at a relatively low price. Fundamentally there wouldn’t be different price of same underlying stock in the different market while market being perfect but if there are two prices for the same security one can have the arbitrage opportunity.
Arbitrage opportunity can also be used to compare the required rate of return & expected return, therefore one short sale the overpriced security or portfolio and also purchase the under price portfolio from the same proceed which was realize from short selling.

Three conditions should be needed in order to grab the arbitrage opportunity
1. In-order to invest, the security or portfolio should be undervalued (Under priced)
2. There should be zero initial cash outlay.
3. There should be zero incremental risk.


Regression Line or equation for arbitrage opportunity
Arbitrage pricing model is similar with the CAPM model. CAPM assume only one risk factor (systematic risk factor or beta) for pricing the assets but APT assumes multiple factors which affects security’s return while pricing the assets. Therefore in APT while pricing the security or determining the required rate of return all those factors need to be consider. These various risk factor are called the macro economic systematic risk factors. The general equation for arbitrage opportunity can be categorized into two parts.

Meaning of Diversification:

Meaning of Diversification:
The process of adding securities to a portfolio in order to reduce the portfolio’s unique risk and thereby the portfolios total risk.

Forms (Techniques) of Diversification:
a) Simple Diversification:
“Not putting all eggs in one basket”
In simple diversification, securities are selected added on random basis for making portfolio. Simple diversification reduces a portfolio’s total diversifiable risk to zero and only the undiversifiable risk remains. It is found that 10 – 15 securities are sufficient for a portfolio to minimize the portfolio’s total risk to the undiversifiable level.

b) Diversification across industries
In this diversification portfolio is constructed by selecting assets from different industries rather than from one industry. For eg if someone selects the securities from hotel banking, insurance co’s and other industries to make portfolio then it is called diversification across industries. But, empirical research has shown that diversifying across industries is not much better than simple selecting securities randomly.

c) Superfluous diversification
From research study, it is found that 10 – 15 assets in the portfolio are sufficient for risk diversification. But if more than 10 – 15 assets are added in the portfolio then such diversification is called superfluous diversification. It should be avoided; superfluous diversification will usually result in the following portfolio management problems:

1. Impossibility of good portfolio management
2. High search cost
3. High transaction cost

d) Simple diversification across quality rating
Some rating agencies rate different companies and their assets on the basis of the possibility of default risk (the risk of bank rupt) Under this categories we select assets randomly from the homogeneous quality ratings. The highest quality portfolio (of randomly diversified stocks) will be able to achieve lower levels of risk than the simple diversified portfolio of lower quality stocks.

e) Markowitz Diversification
Markowitz Diversification may be defined as combining assets which are less than perfectly positively correlated ( i.e. ≤ + 1 ) in order to reduce portfolio risk without sacrificing portfolio returns. Markowitz diversification is more analytical than simple diversification and considers assets correlations. The lower the correlation between assets, the more than Markowitz diversification will be able to reduce the portfolio’s risk. Therefore the Markowitz diversification focuses on the correlation between assets.




Expected Return of Portfolio E ( rp )
Expected return of the portfolio is defined as weighted average expected returns of assets. The portfolio where the proportion of investments on each assets are used as weight.

Market Index

Market Index

Securities market index are construct to get the answer of following questions; “What is the market doing?”, “What did the market do yesterday?” Index number is devoid of dollar values or other units of measure. Stock market index are “pure number” use for marketing composition between different index numbers in the same series of other index number. Market index are also know as the indicator of the movement of the overall securities prices in the secondary market.

E.g.

Nepal Stock Exchange (NEPSE)

Dow Jones Industrial Average (DJIA)

Standard & Poor 500 Index

Market index furnish a handy summary of historical price levels in their specific markets, especially when they are presented in graphical form. By the use of index, investors who own several securities in a give market or industry can quickly get an indication of how mkt movements have affected the value of their portfolio. Similarly, indexes are useful for historical analysis. By analyzing mkt indexes and other economic indicators, an analyst may detect some consistent relationship between different indexes and the fortunes of sectors of the economy.

Methods of Calculating Index:

There are four most popular methods to compute market index. They are:

1) Price Weighting:

The Dow Jones Industrial Average is calculated by using this method. In this method index is calculated by summing the prices of the stocks that are included in the index and ends by dividing this sum by a constant (called Divisor). Mathematically, the formula is:

Specifically, the equation for calculating index by price weighting method is

2) Value Weighting:

In this method, index is computed daily by multiplying price of the stock index and their respective number of shares outstanding and then added up in order to arrive at a figure equal to the aggregate market value for that day. This figure is then divided by the corresponding figure for the day zero (the index was started) with the resulting value being multiplied by an arbitrarily determined beginning index value i.e.

3) Equal Weighting:

This is index is computed by multiplying the level of the index on the previous day by the arithmetic mean of the daily Price Relatives (Today’s Price/Yesterday’s Price) of the relevant stocks in the index i.e.