Question

Portfolio Analysis​​​​​​​​​​

i) Briefly describe the main two Types of Risk of an Investor and state the factors generating those Risks. ​​​​​​​​​​

ii) Briefly explain CAPM and Coefficient of Systematic Risk - Beta. Also state the 3 types of Beta with one liner definition. ​​​​​​​​​

iii) Briefly explain how an Efficient Portfolio reduces the Risk of an Investor.​​

iiii) Security A has an expected Return of 20% and standard deviation of 25% whereas Security B has an expected Return of 30% and standard deviation of 35%.

The Covariance of the Returns on these two securities is 230

Requirement​​​​​​​​​​

Determine the expected Return & Risk of a Portfolio made up of 30% of A and 70% of B.

v) If the Average Variance of securities is 280 and the Average Co Variance is 150.

Requirement​​​​​​​​​​

Determine the expected Risk of an Equally Weighted Portfolio made up of 50 Securities.

Answer 1

i) Types of Risk faced by the Investor -

Market Risk - This is the risk that the investments might decline in value because of factors that affect the entire market, Example - increase in interest rates (while you're invested in a financial instrument that provides a lower interest rate) or change in the exchange rates (applies to the investor's foreign investments).

Liquidity Risk - This is the risk faced by an investor by way of which he can not unwind his position at a fair price. To sell the investment, a lower price has to be accepted.

ii) CAPM stands for Capital Asset Pricing Model.

It describes the relationship between the expected return and the risk of investing in the particular security. The CAPM equation is -

E(R) = Rf + (Rm- Rf) B

where,

E(R) = Expected Return

Rf = Risk - Free Rate Of Return

Rm - Market Rate Of Return

B = Beta or systematic risk

The model recognizes that the return on an investment should increase as the risk involved does. If no risk is involved, only the risk-free rate of return is earned.

However, if risk is taken, the investor has to be compensated for risk that is being taken over and above the risk of the market which is measured by the Beta/Systematic Risk.

For example, if an investor's position has a Beta of 1.1 as compared to the market that has a Beta of 1, with the market rate of return being 20$ and Risk-free Rate being 10$, he will be compensated for the extra risk involved in this manner -

= 10 + (20-10)*1.1

= 10 + 11

= 21

Beta is used to measure the sensitivity of the investment to that of the market. It is the measure of volatility of the security as compared to the market or some other benchmark.  For example - If Beta = 1.5, it means that the security is 50% more volatile/riskier than the market and the investor expects to be rewarded for it.

3 types of Beta with one linear definition -

Beta > 1 - This means that the security's price is more volatile than that of the market and hence, a return expected on this security should be more than that of the market. It is said to be riskier than the market.

Beta = 1 - This means that the security's price is as volatile as that of the market. Hence, the return is going to be exactly the same as that of the market as the risk involved is equivalent to that of the market. No risk greater than it is being taken, hence no extra compensation required either.

Beta < 1 - This means that the security's price is less volatile than that of the market. Hence, the return expected should be lesser than that of the market. It is said to be less riskier than the market.

iii) The efficient frontier is a set of portfolios that offers the highest expected return for a given level of risk or the lowest risk for a given level of return that is expected. All the portfolios that lie below the efficient frontier are sub-optimal because they either involve a higher level or risk for a given level of return or a lower level of return for a given level of risk. As we can see, any point below the efficient frontier will not be chosen as a portfolio option as the ones on the line have a lower risk involved for the same level of return.

iiii) Expected Return :

where W = weight of the securities 1 and 2 in the portfolio

R = expected returns of the securities 1 and 2 in the portfolio  

= 30%*20 + 70%*30

= (6 + 21)%

= 27%

The calculation for risk of the portfolio has been shown above.

Sigma is the standard deviation of the securities.

We have been asked to find the risk/volatility, which is the square root of the variance as shown.

v) The formula and calculations for an equally weighted portfolio is shown below -