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
