Portfolio Theory and Asset Models - Accounting & Finance Assignment Help

Assignment Task

Questions
1. Calculate the covariance matrix C = (?ij ).
2. Find the minimum variance portfolio A, ?A (that is, the optimal proportions, (?1, . . . , ?5)), subject to P5i=1 ?i = 1.
Show your working.
3. Calculate the mean, µA, and standard deviation, ?A, of the return, RA, on the minimum variance portfolio.
Show your working.
4. Find the minimum variance portfolio B, ?B, subject to an expected return of 7%, and subject to P5i=1 ?i = 1.
Show your working.
(Hint: You should find that the proportion invested in asset 1 is 0.436 rounded to 3 decimal places.)
5. The minimum variance frontier can be written as (?P , µP )
where: ?2
P = ?2A + k(µP ? µA)2 for µP ? µA, and µA and ?A have been derived in question 3 above. Find the value of k.
Show your working.
(Hint: first find k in terms of µA, µB, ?2 A and ?2 B. Then find the numerical value of k.)
6. For this question assume, in addition to the information given above, that R1, . . . , R5 have a multivariate normal distribution. (Hence, portfolio returns, RP , are also normally distributed.)
An investor uses value-at-risk to measure risk.
(a) A given portfolio, P, has mean return µP and variance ?2 P.
i. What is the distribution of the loss per £100 invested?
ii. Written in terms of µP and ?P , what is the value-at-risk for this portfolio at a 97.5% confidence level?

(b) Solve the following problem:
• Maximise the mean portfolio return, µP , subject to
• Constraint 1: P5 i=1 ?i = 1;
• Constraint 2: the value-at-risk with a confidence level of 97.5% per £100 invested should be less than or equal to £5.
Your solution should identify the composition of the optimal portfolio ?P , along with the mean, standard deviation and value-at-risk.
Show your working.

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