The volatility of SBN company is 1.5% per day and the size of the position is $6
ID: 2826823 • Letter: T
Question
The volatility of SBN company is 1.5% per day and the size of the position is $6 million. Assuming that the change is normally distributed, find a one-day 97% VaR and 10-day 90% VaR.Consider a portfolio consisting of $4 million invested in Stock Fund and $6 million in Bond Fund. The daily volatility of Stock Fund is 1% and the daily volatility of Bond Fund is 2%. The correlation coefficient between two funds is -0.4 and they are normally distributed.
A.) Find the 10-day 99% VaR.
B.) Find the diversification benefit. The volatility of SBN company is 1.5% per day and the size of the position is $6 million. Assuming that the change is normally distributed, find a one-day 97% VaR and 10-day 90% VaR.
Consider a portfolio consisting of $4 million invested in Stock Fund and $6 million in Bond Fund. The daily volatility of Stock Fund is 1% and the daily volatility of Bond Fund is 2%. The correlation coefficient between two funds is -0.4 and they are normally distributed.
A.) Find the 10-day 99% VaR.
B.) Find the diversification benefit.
Consider a portfolio consisting of $4 million invested in Stock Fund and $6 million in Bond Fund. The daily volatility of Stock Fund is 1% and the daily volatility of Bond Fund is 2%. The correlation coefficient between two funds is -0.4 and they are normally distributed.
A.) Find the 10-day 99% VaR.
B.) Find the diversification benefit.
Explanation / Answer
1.
VaR for 97% Confidence level (Please refer Z values from normal distribution table)
10-day VaR for SBN = Portfolio value x Standard deviation daily x Z-score for 97% confidence level x Days^0.5
10-day VaR for SBN = $6000000 x 1.5% x 1.880793608 x 10^0.5
10-day VaR for SBN = $535,283.24
.
VaR for 90% Confidence level
10-day VaR for SBN = Portfolio value x Standard deviation daily x Z-score for 90% confidence level x Days^0.5
10-day VaR for SBN = $6000000 x 1.5% x 1.281551566 x 10^0.5
10-day VaR for SBN = $364,735.97
.
2.
Standard Deviation of portfolio when Corr = -40%
Standard deviation of stock = SdA = 1% ; Standard deviation of bond = SdB = 2%;
Weight of stock = wA = 40% ; Weight of bond = wB = 60%
Applying below standard deviation of portfolio formula:
Standard Deviation of portfolio = (wA^2*sdA^2+wB^2*sdB^2+2*Corr*wA*sdA*wB*sdB)^0.5
Standard Deviation of portfolio = (40%^2*1%^2+60%^2*2%^2+2*-40%*40%*1%*60%*2%)^0.5
Standard Deviation of portfolio = 1.102724%
.
10-day VaR of portfolio at 99% confidence level = Portfolio value x Standard deviation daily x Z-score for 99% confidence level x Days^0.5
10-day VaR of portfolio at 99% confidence level = 10,000,000 x 1.102724% x 2.326347874 x 10^0.5
10-day VaR of portfolio at 99% confidence level = $811,225.30
.
…………….
Diversification benefit = VaR of stock + VaR of Bond – VaR of Portfolio
Individual VaR:
VaR of stock = Stock value x Standard deviation daily x Z-score for 99% confidence level x Days^0.5
VaR of stock = 4000000 x 1% x 2.326347874 x 10^0.5
= $294,262.32
.
VaR of Bond = Bond value x Standard deviation daily x Z-score for 99% confidence level x Days^0.5
VaR of Bond = 6000000 x 2% x 2.326347874 x 10^0.5
VaR of Bond = $882,786.95
.
Question is not clear on diversification benefit ...Hence I am adding each portfolio other wise same can be worked out taking 100% investment in stock or 100% in bond. Please advise if such thing has to be done here.
Otherwise below is appropriate:
Diversification benefit = $294,262.32 + $882,786.95 - $811,225.30
Diversification benefit = $365,823.97
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.