Question

11. A client has a portfolio of common stocks and fixed-income instruments with a current value of £1,350,000. She intends to liquidate £50,000 from the portfolio at the end of the year to purchase a partnership share in a business. Furthermore, the client would like to be able to withdraw the £50,000 without reducing the initial capital of £1,350,000. The following table shows four alternative asset allocations.

Mean and Standard Deviation for Four Allocations (in Percent)

  

A B C D

Expected annual return 16 12 10 9

Standard deviation of return 24 17 12 11

Address the following questions (assume normality for Parts B and C):

1. Given the client's desire not to invade the£ 1,350,000 principal, what is the shortfall level, RL? Use this shortfall level to answer Part B.

2. According to the safety-first criterion, which of the allocations is the best?

3. What is the probability that the return on the safety-first optimal portfolio will be less than the shortfall level, RL?

Answer 1

A. Since £50,000/ £1,350,000 is 3.7%, for any return less than 3.7% the client will need to invade principal if she takes out £50,000.

So RL= 3.7 %

B. To decide which of the three allocations is safety-first optimal, select the alternative with the highest ratio

[E (RP ) − RL ] / σP :

Allocation A: = (16 − 3.7) / 24 = 0.5125

Allocation B: = (12 − 3.7) / 17 = 0.4882

Allocation C: = (10 − 3.7) / 12 = 0. 5250

Allocation D: = (9 − 3.7) / 11 = 0. 4818

Allocation C, with the largest ratio (0.5250), is the best alternative according to the safety-first criterion.

C. Pr(RC< RL)

= Pr(RC< 3.7)

= Pr[Z< (3.7-10)/12]

= Pr(Z < -0.53)

= 0.2981

There is 29.81% chance that the return would be less than the shortfall rate andhence the principal would be invaded