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In: Finance

Assume that you manage a risky portfolio with an expected rate of return of 12% and...

Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 44%. The T-bill rate is 5%. Your client chooses to invest 80% of a portfolio in your fund and 20% in a T-bill money market fund.


a.

What is the expected return and standard deviation of your client's portfolio? (Enter your answer as a percentage rounded to two decimal places.)


  Expected return % per year  
  Standard deviation % per year


b.

Suppose your risky portfolio includes the following investments in the given proportions:
  Stock A 28%
  Stock B

37%
  Stock C 35%


What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Enter your answer as a percentage rounded to two decimal places.)


Security     Investment
  Proportions
  T-Bills    %
  Stock A    %
  Stock B    %
  Stock C    %


c.

What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Enter your answer as a decimal rounded to 4 decimal places.)


Reward-to-Volatility Ratio
  Your risky portfolio            
  Client’s overall portfolio            

Solutions

Expert Solution

a

Weight of Risky portfolio = 0.8
Weight of T bill = 0.2
Expected return of Client portfolio = Weight of Risky portfolio*Expected return of Risky portfolio+Weight of T bill*Expected return of T bill
Expected return of Client portfolio = 12*0.8+5*0.2
Expected return of Client portfolio = 10.6
Weight of Risky portfolio = 0.8
Weight of T bill = 0.2
Std dev of Client portfolio = Weight of Risky portfolio*Std dev of Risky portfolio+Weight of T bill*Std dev of T bill
Std dev of Client portfolio = 44*0.8+0*0.2
Std dev of Client portfolio = 35.2

b

Weight of T bill = 20%

Weight of stock A = Weight of risky portfolio*weight of stock A in risky portfolio=0.8*0.28=22.4%

Weight of stock B = Weight of risky portfolio*weight of stock B in risky portfolio=0.8*0.37=29.6%

Weight of stock C = Weight of risky portfolio*weight of stock C in risky portfolio=0.8*0.35=28%

c

Risky portfolio

Sharpe ratio(reward to variability)
=(Return-risk free rate)/std dev
=(12-5)/44
=0.1591

Client portfolio

Sharpe ratio(reward to variability)
=(Return-risk free rate)/std dev
=(10.6-5)/35.2
=0.1591

jeff jeffy answered 4 months ago
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