**A portfolio **is a collection of assets such as

stocks, bonds, real estate, etc.

**The return to a portfolio **of assets is an

average return of all of the assets, weighted

by the relative amount invested in each

asset. However, the risk of a portfolio of

assets is fundamentally different from the

average risk of all assets in the portfolio.

**Correlation ****measures** the tendency for the

returns of two assets to move together. In

technical terms, it measures the strength

and direction of the linear relationship

between two variables.

** ANSWER 1
**

**(a) Challenges in the application of the CAPM in practice**

– The need to determine the excess return (E(Rm) – Rf i.e the premium means that a

market portfolio should be identified and used as a benchmark. This is very difficult.

– The need to determine the risk-free rate. A risk free investment might be a

government security. However, interest rates vary with the term of the lending. In

reality, a risk-free asset does not exist. Even government bonds, actually contain

risk.

– Error in the statistical analysis used to calculate Beta Values. Beta may also change

over time.

– The model is only based on forward-looking data for example expected rate of return

and expected beta. Obviously, these cannot be estimated with precision and are

therefore often historically based.

– Lack of free and instantly available information (information market efficiency) and

the exclusion of taxes and transaction costs. Could lead to erroneous predictions.

– It is unrealistic to expect all investors to have homogeneous expectations and that

they all act rationally, based on the expected return and the standard deviation.

**ANSWER 2
**

**(a)Explain why it is argued that only systematic risk and not total risk is**

**important.**

Total risk is an amalgamation of systematic risk and the unsystematic risk. However,

as investors invest in more than one company, that is portfolio, the unsystematic risk

is eliminated and therefore, the only relevant risk component that will determine the

return is the systematic risk and that is why we consider systematic risk only.

CAPM is the model that works with systematic risk to evaluate portfolio security

returns.

** ANSWER 3
**

**a)“Corporate diversification and conglomerate mergers are an experiment in**

**portfolio theory applied to corporations”. Explain the above statement**.

– Corporate diversification refers to the combination of two businesses with less than

perfectly correlated cash flows which create a merged firm with less volatile cash

flows and inherently lower business risk, where bad outcomes in one business can

be offset by good outcomes in another business.

– Diversification supporters contend that these less volatile cash flows make debt

services less risky lowering default risk and the required rate of return on debt.

b) Explain how each of the following portfolio performance measures are used:

i) Treynor’s ratio;

Trenor was the first scholar to develop a composite measure of portfolio performance.

This measure is based on the background of CAPM and therefore it operates

effectively under the assumptions of CAPM. This means that the weaknesses/

drawbacks of Treynor’s measures are similar to weakness of CAPM.

Treynor’s measure of portfolio performance involve computing a T value of portfolio

using beta factors.

Jensen’s alpha

It is a risk-adjusted performance measure that represents the average return on

a portfolio over and above that predicted by the capital asset pricing model

(CAPM), given the portfolio’s beta and the average market return. This is the portfolio’s

alpha.

This is an improvement of Treynor’s measure of portfolio performance. It uses the

CAPM to calculate Beta factors to evaluate portfolios. We normally calculate

profitability indices. Known alpha values (𝛼)

If 𝛼 is positive, the performance of a portfolio is superior.

If 𝛼 is negative, the performance of a portfolio is inferior.

If 𝛼 =0, indicates efficient.

ANSWER 4

a) Difference between CAPM and APT

CAPM | APT |

• CAPM uses indifference curves in determining utility of investors and in identification of market portfolios. • Considered to be less general and unrealistic since only one factor |
• APT doesn’t make use of indifference curve in determining utility of investors. • Its Considered to be more general and realistic in estimating returns of securities since it considers all factor that cause systematic risk. |

will be used to analyse systematic risk. • It assumes normal distribution of returns • CAPM is a single factor model • It assumes that a well-diversified portfolio exists. • It’s a single period model applicable for relatively short duration of investment. |
• It assumes returns are generated through continuous trading. • It is a multi-factor model. • Ignores assumptions of a well diversified portfolio. • Can be extended to multi-period framework. |

**ANSWER 5
**

**a) Evaluation of assumptions on which the capital asset pricing model (CAPM)**

**is based**

⎯ Investors are rational and require greater returns for taking greater risks.

⎯ There are no market imperfections. The market imperfections of lack of divisibility

of investments, fixed charges, imperfect opportunities and imperfect information

means that the model has poor predictive ability.

⎯ The model ignores the risks of insolvency – which must be considered by investors.

⎯ Assumes that the expectations are homogeneous – clearly, not all investors have the

same view on the prospects of securities. However, when this assumption is relaxed,

the CAPM has still been found to maintain its predictive abilities.

⎯ It assumes that there is no inflation – Inflation clearly exists and may be seen as an

additional risk. However, when incorporated into the model, the model can still

predict the required returns accurately.

⎯ Investors are able efficiently to diversify away unsystematic risk. There are many

reasons why investors may not diversify enough as required by CAPM. It requires

effort and huge resources for an investor to manage a portfolio of investments

actively. Investors may not want to diversify from a business that they know well.

Similarly, investors may not wish to be restrained from “playing the market”,

whatever the arguments in favour of diversifying away risk.

⎯ There are no transaction costs – the existence of transaction costs means that

investors may not undertake all required transactions to make their portfolios

efficient.

⎯ CAPM assumes that there are equal borrowing and lending rates. Generally,

borrowing rates are higher than lending rates.

QUESTION 6

**Evaluate any four limitations of portfolio analysis.**

Limitations of portfolio analysis

⎯ Portfolio model assumes that investors have unlimited access to borrow and lend

money at risk free rate.

⎯ It assumes that investors have access to the same sources of information. This is

not practical.

⎯ Assumes that investors are rational and avoid risk. There are types of investors for

instance risk takers.

⎯ Shareholders preferences between risk and return may be difficult to determine

⎯ It is difficult to estimate the probabilities of occurrence of given outcomes

⎯ The portfolio theory assumes that there is constant return to scale i.e that the

returns remain constant regardless of how much has been invested.

⎯ Projects may be of such a size that they are not easy to divide in accordance with

recommended diversification principles.

⎯ Other aspects of risk are not covered by the theory e.g. bankruptcy costs