Question

13)

Consider a Treasury bill with a rate of return of 5% and the following risky securities:

Security A: E(r) = .15; variance = .0400

Security B: E(r) = .10; variance = .0225

Security C: E(r) = .12; variance = .1000

Security D: E(r) = .13; variance = .0625

The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of her complete portfolio to achieve the best CAL would be _________.

Multiple Choice

• security A

• security B

• security C

• security D

Answer 1

Given the following information,

Security	Expected return	Variance
A	0.15	0.0400
B	0.10	0.0225
C	0.12	0.1000
D	0.13	0.0625

Since the portfolio consists of a treasury bill and one of the above securities we need to compute which one of the above securities is less risky.

In order to know the lowest risky security we need to know which one is having the minimum volatility for this we need to calculate the coefficient of variation (CV), which is given by the following formula,

Coefficient of variation (CV) = Standard Deviation/ Expected return

In case of security A:

CV = SD/ E(r)

Where,

SD = Squaroot(variance)

SD = Squaroot(0.0400)

SD = 0.20

CV = 0.20/ 0.15

CV = 1.33

In case of security B:

CV = SD/ E(r)

Where,

SD = Squaroot(variance)

SD = Squaroot(0.0225)

SD = 0.15

CV = 0.15/ 0.10

CV = 1.50

In case of security C:

CV = SD/ E(r)

Where,

SD = Squaroot(variance)

SD = Squaroot(0.1000)

SD = 0.32

CV = 0.32/ 0.12

CV = 2.64

In case of security D:

CV = SD/ E(r)

Where,

SD = Squaroot(variance)

SD = Squaroot(0.0625)

SD = 0.25

CV = 0.25/ 0.13

CV = 1.92

Security	Expected return	Variance	Coefficient of variation
A	0.15	0.0400	1.33
B	0.10	0.0225	1.50
C	0.12	0.1000	2.64
D	0.13	0.0625	1.92

Since the security A is having the lowest CV will have the minimum volatility hence minimum risk, the investor should Security A as a per of her portfolio along with the treasury bill.

Therefore, the answer is Security A