INVESTMENT ANALYSIS - EXAM QUESTION

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ILLUSTRATION:

What are the assumption underlying the capital asset pricing model (CAPM)?

Explain its imitations and how it differs from the arbitrage pricing theory.

ASSUMPTIONS OF CAPITAL ASSET PRICING MODEL (CAPM)

The capital asset pricing model is developed on a number of assumptions. The following are most important assumptions ( pandey, 1999).

·         Capital market efficiently, which implies that security prices reflect all available information, no taxes , regulations or floatation

·         Investors are risk-averter. When faced with a choice of the portfolio having the same expected return, they pick the portfolio with the lowest standard deviation.

·         Homogenous expectations, which imply that all investors have the same expectations about the risk and expected return of securities.

·         Single time period, which means that all investor’s decisions are based on single time period.

·         Risk-free rate, which means that all investors can lend or borrow at a risk-free rate of interest.

·         All investors analyze securities in the same way and share the economic view of the world.

LIMITATIONS OF CAPM

1.       INSTABILITY OF BETA:

Beta is a measure of non-diversifiable risk. Beta does not remain stable over time which makes it difficult for measurement of future risk of security because investors have only historical data that cannot be very much relevant for the future occurrence.

2.       UNREALISTIC ASSUMPTION:

CAMP is based on unrealistic assumptions. For instance, in reality there is no such thing as risk free security, except government short term bonds which are highly liquid. Also the assumption is equality on lending and borrowing rates may not be correct.

3.       DIFFICULT TO VALIDATE:

It is difficult to test the validity of CAMP. For instance, the empirical validity of CAPM is able to measure the risk of a security and that there is a significant correlation between beta and expected return. Empirical results have given mixed results.

4.       Many a times, the risk of a security is not captured by beta alone as assumed by CAPM.

Note: However, notwithstanding the limitations of CAPM, it is still a useful devise for understanding the risk –return relationship of securities.

	CAPM	ABRITAGE P.M
i.	CAPM is not one factor model (i.e. single beta generating model)	APM is a multi-factor model (multi beta model)
ii.	CAPM assumes that all investors are rational mean-variance optimizers, meaning that, they all use the Markowiz Portfolio selection model	APM does not assume that investors employ mean-variance analysis for their investment decisions.
iii.	All investors plan for one identical holding period, in that it ignores everything that might happen after the end of the single period horizon.	It is not restricted to a single period. It will hold in both the multiple and single period cases.
iv.	In CAPM, it is assumed that the risk of a security is measured by beta alone.	In APM, there may be one or more macro-economic variables that may measure the systematic (unavoidable) risk of a security).

Even though multiple beta are considered in APM, which makes it appealing, despite the appeal of APM, it has not displaced the use of CAPM in corporate finance.

However, APM also like CAPM is founded on the notion that investors are compensated for assuming undiversifiable risk is not rewarded.

ILLUSTRATION:

Distinguishing between the Capital Market Line and the Security Market Line

 

THE EFFICIENT FRONTIER AND THE CAPITAL MARKET LINE

The Capital market Line (CML) is the line from the risk free rate (R_F) through the market portfolio, M. the line RFMX is termed CAPITAL MARKET LINE as it represents the market equilibrium tradeoff between risk and return.

The CML graphs the premium of efficient portfolio (i.e. portfolio composed of the market and the risk – free asset) as a function of portfolio standard deviation. This is appropriate because standard deviation is a valid measure of risk for efficient diversified portfolio that is candidates for an investor’s overall portfolio.

The Capital Market line equation as follows:

CML = E(R_P) = R_F + [E(R_M) – R_F] σP

σm

E(R_P) = Expected return on the portfolio

Rf = Risk free securities

Rm = Expected return on the risky market portfolio

σp = Standard deviation of the portfolio

σm = Standard deviation of the risky market portfolio

SECURITY MARKET LINE

The SML in contrast, graphs individual asset risk premiums as a function of asset risk. The relevant measure of risk for individual asset held as parts of well diversified portfolio is not the asset’s standard deviation or variance. It is, instead, the contribution of the asset to the portfolio variance, which we measure by the asset’s beta.

The SML is valid for both efficient portfolio and individual asset.

The SML provides a benchmark for the evaluation of investment performance.

The security market line equation is expressed as follows:

E(Ri) = Rf + βi [E(Rm) – Rf)]

E(Ri) – Expected return on security

Rf = The risk free rate

E(Rm) = The Expected return on the market portfolio

Βi = rep. the portion of the market risk that is embedded in the securities

QUESTION:

Compare the CML to the SML

SOLUTION:

The CML graphs the risk premium of efficient portfolio (i.e. portfolios composed of the market and the risk – free asset) as a function of portfolio standard deviation. This is appropriate because standard deviation is a valid measure of the risk for efficiently diversified portfolios that are candidates for an investor’s overall portfolio. The SML in contrast, graphs individuals assets risk premium as a function of asset risk. The relevant measure of risk for individual asset held as parts of well diversified portfolio is not the assets standards deviation or variance. It is instead, the contribution of the portfolio variance, which we measure by the asset beta. The SML is valid for both efficient portfolios and individual assets.

The SML provides a benchmark for the evaluation of investment performance. Given the risk of an investment, as measure by its beta, the SML provides the region rate of return from that investment to compensate investor for risk, as well as the time value for money.