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In: Finance

Consider two assets. Suppose that the return on asset 1 has expected value 0.06 and standard...

Consider two assets. Suppose that the return on asset 1 has expected value 0.06 and standard deviation 0.15 and suppose that the return on asset 2 has expected value 0.03 and standard deviation 0.08. Suppose that the asset returns have correlation 0.35.

Consider a portfolio placing weight ω on asset 1 and weight 1-ω on asset 2. Let Rp denote the return on the portfolio.

  1. Find the mean, variance, and standard deviation of Rp as a function of ω. Display your output
  2. Plot the opportunity set
  3. Find the minimum-variance portfolio. Report the weights, mean, and standard deviation of this portfolio.
  4. Find the tangency portfolio. Suppose the risk-free rate is 0.003. Report the weights, mean, and standard deviation of this portfolio.

Solutions

Expert Solution

R1 = Return on asset 1 = 0.06

R2 = Return on asset 2 = 0.03

= Standard Deviation of asset 1 = 0.15

= Standard Deviation of asset 2 = 0.08

= weight of asset 1

= weight of asset 2

= variance

Return is also called as mean.

(a.)

  

  

  

OR   

  

  

  

  

  

  

  

(b.) apply same formula for calculating return of portfolio and standard deviation use above.

Set of possible portfolios that may construct from a given set of assets. One can construct both high - and - low - risk portfolios from an opportunity set. Opportunity set may help in making investment decision.

(c.)

Minimum variance Portfolio has minimum risk with high return.

For this firstly we have to calculate weights for the assets in the portfolio.

Weight of Asset 1 = w1

Weight of Asset 2 = w2

  

  

= 0.1073 or 10.73%

  = 1 - 0.1073 = 0.8927 or 89.27%

= 0.06 * 0.1073 + 0.03 * 0.8927

= 0.006438 + 0.026781

= 0.033219 or 0.0332

  

= (0.016095)2 + (0.071416)2 + 0.00080460836

= 0.0002590 + 0.0051002 + 0.0008046

= 0.0061638 or 0.0062

= 0.07851 or 0.0785

(d.) tangency portfolio is a portfolio having risk free asset.

  

  

= 0.5942 Or 59.42%

= 1 - 0.5942

= 0.4058 Or 40.58%

= 0.4058 * 0.06 + 0.5942 * 0.03

= 0.024348 + 0.017826

= 0.042174 Or 0.0422

= (0.15 * 0.4058 )2 + ( 0.08 * 0.5942 )2 + 2 * (0.15 * 0.4058 ) * ( 0.08 * 0.5942 ) * 0.35

= 0.0037052 + 0.0022597 + 0.0020255

= 0.0079904 Or 0.00799

=

= 0.08939

jeff jeffy answered 2 years ago
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