Question

A) Differentiate between perfect negative correlation and perfect positive correlation.

B) Explain the concept of diversification in investment portfolio.

C) What are the two (2) advantages of Payback Period?

D) Amaryllis Incorporated is attempting to evaluate the feasibility of investing RM95,000 in a piece of equipment that has a 5-year life. The firm has estimated cash inflows

associated with the proposal as shown in the following table. The firm has a 12% cost of capital.

Answer 1

1. Perfectly Negative correlation has Correlation Coefficient =-1.

Asset A and Asset B can be said to be perfectly negatively correlated if with 5% increase in value of Asset A , there is 5% Decrease in value of asset B. Increase in value of one asset ,there is same percentage decrease in value of the other assets.

For example , Gold and Stocks are generally negatively correlated. If there is decrease in value of stocks, the capital moves towards a safer asset of gold that results in increase in price of gold

Asset X and Asset Y can be said to be perfectly Positively correlated if with 5% increase in value of Asset X , there is 5% Increase in value of asset Y. Increase in value of one asset ,there is same percentage decrease in value of the other assets.

For example , two technology stocks are generally positively correlated. If there is decrease in value of one technology stock, there is decrease in value of other stock.

Perfectly Positive correlation has Correlation Coefficient =+1

B.CONCEPT OF DIVERSIFICATION IN INVESTMENT PORTFOLIO

There is an old saying “Do not put all eggs in one basket”

Why?

Because risk is high.By keeping eggs in different baskets, we reduce risk

We try to do same thing through diversification.

By investing our capital in different assets , we try to reduce risk.

Diversified folios reduce the risk and also the ratio of Risk to reward.

If w1, w2 , w3 …wn are weight in the portfolio for assets 1, 2,3 ….n

Then,w1+w2+w3+……………………+wn=1

R1, R2,R3,…….Rn are the return of the assets 1, 2 , 3 ….n

S1, S2, S3……Sn are the standard deviation of the assets 1, 2, 3 …n

Portfolio Return=w1R1+w2R2+w3R3+…….+wnRn

Portfolio Variance=(w1^2)*(S1^2)+(w2^2)(S2^2)+………….(wn^2)*(Sn^2)+2w1w2*Cov(1,2)+2w1w3*Cov(1,3)+………+w(n-1)wn*Cov(n,(n-1)

Cov(1,2)=Covariance of returns of asset1 and asset2

Portfolio Standard Deviation =Square root of Portfolio variance

Risk of a stock is measured by standard deviation.

Hence reduction of standard deviation through diversification means reduction of risk.

We can take a simple example of two assets 1 and 2

Return of asset1=R1=15%

Return of asset2=R2=12%

Standard deviation of asset 1=S1=10%

Standard deviation of asset 2=S2=8%

Correlation of asset 1 and 2=Corr(1,2)=0.1

Covariance(1,2)=Corr(1,2)*S1*S2=0.1*10*8=8

Assume for simplicity, equal amount is invested in asset 1 and asset 2

Hence, w1=w2=0.5

Portfolio Return;

0.5*15+0.5*12=13.5%

Portfolio Variance=(0.5^2)*(10^2)+(0.5^2)*(8^2)+2*0.5*0.5*8=45

Portfolio Standard Deviation=Square root of Variance=(45^0.5)= 6.708204

We can see, the risk of portfolio as measured by Standard Deviation has reduced significantly to 6,7 whereas the assets in the portfolio had standard deviation of 10 and 8

Risk / Return ratio of the portfolio=6.7/13.5=0.496

Risk/Return ratio of asset1=10/15= 0.666667

Risk/Return ratio of asset2=8/12= 0.666667

Risk return ratio of the portfolio is lower

WHY INVEST IN DIFFERENT TYPES OF ASSETS?

Return of same types of assets are highly correlated. Suppose, if you invest in 10 different Technology Companies, you may not be able to reduce risk, because all the companies will have similar return and highly correlated.

We have seen in the equation of Portfolio Variance, one factor=2 w1*w2*Cov(1,2)

If there is high correlation between return of asset1 and 2, the Covariance(1,2) will be high . Hence this factor 2w1w2Cov(1,2) will be high. As a result portfolio standard deviation will be high and diversification will not serve any purpose.

Hence, in order to get benefit of diversification, we need to invest in different classes of assets such that the correlation between different assets are low, and consequewntly, the portfolio risk (measured through standard deviation) is low.

DISADVANTAGE:

· It requires efforts to track the number of assets and their return

· It costs slightly more to manage

C) Two Advantages of Payback Period

1. It is simple and easy to understand, calculate and communicate to everyone ,specially non finance professionals

2.Payback period is focussed on risk and liquidity. It measures how quickly you get your initial investment back.