Suppose that your firm’s portfolio consists of three assets with normally distri

Question

Suppose that your firm’s portfolio consists of three assets with normally distributed returns. The first asset has an annual expected return of 12 percent and an annual volatility of 15 percent. The firm has a long position of $43 million in that asset. The second asset has an annual expected return of 18 percent and an annual volatility of 27 percent. Your firm has a long position of $100 million in the second asset. The third asset has an annual expected return of 15% and the volatility of 20%. The firm has a short position of $50 million in that asset. The correlations between returns on these assets are given below: ASSET 1 2 3 1 1 2 0.3 1 3 0.27 0.4 1 a. Compute the standard deviation of this firm’s portfolio. b. Compute its 5 percent annual VaR.

Explanation / Answer

Standard Deviation of Portfolio = Square -root of the variance of Portfolio

Variance of a Portfolio = [(Variance of stock A * Weight of Stock A)2 + [(Variance of stock B * Weight of Stock B)2+ (2 x Weight of Stock A x Weight of Stock B x Standard Deviation of Stock A x Standard Deviation of Stock B x Co-Relation coefficient of both stocks)]

Total capital = $50 Million + $30 Million = $80 Million
Weight of first asset in portfolio = $50 Million / $80 Million = 0.625 or 62.5%
Weight of second asset in portfolio = $30 Million / $80 Million = 0.375 or 37.5%

Variance of first asset = (0.30)2 = 0.09
Variance of second asset = (0.15)2 = 0.0225

s2P = [(0.09*0.625)2 + (0.0225*0.375)2 + (2*0.625*0.375*0.30*0.15*0.35)] = 0.010618066

sP = (0.010618066)0.5 = 0.103044002 or 10.3044%

So, standard deviation of this portfolio is 10.3044%

VaR of portfolio:

VaR99% = Portfolio Value x sP x Z-score (For one day period)

$80 Million x 0.103044 x 2.576 = 21.23530752 Million or $21,235,307.52

Note: Z-score for a 99% confidence level is 2.576

VaR for 2 weeks period = VaR for one day period x square root of the number of trading days in the period

=> $21,235,307.52 x 100.5 = $67,151,938.58            (2 weeks has 10 trading days)

So, the VaR with 1 percent annual VaR over two weeks will be $67,151,938.58.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.