Logo
Home Study Material Contact Search
AI Chat FREE
  1. business
  2. finance
  3. a pension fund manager is considering three mutual

A pension fund manager is considering three mutual funds. The first is a stock fund, the...

Free

80.2K

Verified Solution

Question

Finance

A pension fund manager is considering three mutual funds. Thefirst is a stock fund, the second is a long-term government andcorporate bond fund, and the third is a T-bill money market fundthat yields a rate of 5%. The probability distribution of the riskyfunds is as follows:

Expected Return Standard Deviation

Stock Funds (S) 17% 38%

Bond Funds (B) 13 18

The correlation between the fund returns is 0.12. What is theSharpe ratio of the best feasible CAL?

Answer & Explanation Solved by verified expert
4.1 Ratings (827 Votes)

To find the fraction of wealth to invest in Stock fund that will result in the risky portfolio with maximum Sharpe ratio
the following formula to determine the weight of Stock fund in risky portfolio should be used
w(*d)= ((E[Rd]-Rf)*Var(Re)-(E[Re]-Rf)*Cov(Re,Rd))/((E[Rd]-Rf)*Var(Re)+(E[Re]-Rf)*Var(Rd)-(E[Rd]+E[Re]-2*Rf)*Cov(Re,Rd)
Where
Stock fund E[R(d)]= 17.00%
bond fund E[R(e)]= 13.00%
Stock fund Stdev[R(d)]= 38.00%
bond fund Stdev[R(e)]= 18.00%
Var[R(d)]= 0.14440
Var[R(e)]= 0.03240
T bill Rf= 5.00%
Correl Corr(Re,Rd)= 0.12
Covar Cov(Re,Rd)= 0.0082
Stock fund Therefore W(*d) = 0.2342
bond fund W(*e)=(1-W(*d))= 0.7658
Expected return of risky portfolio = 13.94%
Risky portfolio std dev = 17.28%
Sharpe ratio= (Port. Exp. Return-Risk free rate)/(Port. Std. Dev) =(0.1394-0.05)/0.1728 =0.5174
Where
Var = std dev^2
Covariance = Correlation* Std dev (r)*Std dev (d)
Expected return of the risky portfolio = E[R(d)]*W(*d)+E[R(e)]*W(*e)
Risky portfolio standard deviation =( w2A*?2(RA)+w2B*?2(RB)+2*(wA)*(wB)*Cor(RA,RB)*?(RA)*?(RB))^0.5

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Chemistry
1.2K views

Calculate the pH when 2.63 g of C6H5COONa is added to 41 mL of 0.50 M...

Psychology
1.2K views

how have psychologists participated in the advancement of social issues? ideas from By David B . Baker

Advance Math
1.2K views

Minimum 320 words and unique content please. In your opinion, what is the most important aspect...

Basic Math
1.2K views

Smudge pots are sometimes used to protect orchards from frost. Two types of smudge pots are...

Physics
1.2K views

our different liquids each of mass 1 kg are separately heated at the same rate...

Basic Math
1.2K views

8 Identify three financial considerations during retirement

Calculus
1.2K views

1 point Rebecca has 45 coins all nickels and dimes The total value of the...

Accounting
1.2K views

Problem 13-3 Current-noncurrent classification of debt [LO13-1, 13-4] The balance sheet at December 31, 2018,...

Accounting
1.2K views

The Prepaid Rent account had a $5,300 debit balance at December 31 before adjusting for...

Accounting
1.2K views

Since budgets affect many people in an organization, they can have significant behavioural implications. Allowing...

Accounting
1.2K views

5.10 The following are the financial statements of Good Services Bhd. Good Services Bhd Statement...

Accounting
1.2K views

On January 2, 2015, Alvarez Company purchased an electroplating machine to help manufacture a part...