Question

Consider the following 2 securities with:

• Expected rate of return on security 1 = 15%
• Expected rate of return on security 2 = 5%
• Variance of security 1 = 225
• Variance of security 2 = 100

Assume the coefficients of correlation are:

-1.0, -0.75, -0.5, 0, 0.5, 0.75, 1.0

1. You have to select a security for investment which one will you select?
2. If you have to obtain the Global minimum variance portfolio for each coefficient of correlation, what will be your investment fractions?
3. Which of the combinations which you obtain in b, give you a diversified portfolio. Check whether the conditions for diversification are satisfied.

Answer 1

Answer-(a)

Standard Deviation =

Coefficient of Variation =

	A	B	C= Sqrt(B)	C/A
Security	Expected rate of return(E(R))(In %)	Variance	Standard Deviation(In %)	Coefficient of variation
1	15	225	15	1
2	5	100	10	2

If one security to be selected then Security 1 should be selected as its Coefficient of variatio is less[ means it will provide higher return with lower risk or standard deviation].

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Answer(b)

When we have two risky assets Security 1 & 2, then

optimal Weight of secirity 1 =

Weight of security 2 = 1- Weight of security 1

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Answer-c

Expected Retun on portfolio =

Standard Deviation on Portfolio =

W1 = Weight of security 1

w2= weight of security 2.

Combination 1 [ Security- 1 40% and Security -2 60%] , gives a diversified portfolio.

Because it gives Gighest Return of 9% at Zero risk.

condition for diversification says that , the less the Correlation between asset, the more is the Diversification and the less is the risk or standard eviation.

Combination 1 has lowest Correlation or -1.0[ Perfectly uncorrelated] and it gighest return with zero Standard deviation.