Question

a. The current value of a stock portfolio is $23 million. A financial analyst summarizes the uncertainty about next year's holding-period return using the scenario analysis in the following spreadsheet. What are the annual holding-period returns of the portfolio in each scenario? Calculate the expected holding-period return, the standard deviation of returns, and the 5% VaR. What is the VaR of a portfolio with normally distributed returns with the same mean and standard deviation as this stock? D End of-Year Value (S million) Annual Dividend million) Business Conditions. Probability. p Scenario, s 4.40 High growth Nomal growth 0.30 35 2 3 045 27 4.00 No growth 020 15 4 4.00 5 Recession 4 0.05 8 2.00 b. Suppose that the worst three rates of return in a sample of 36 monthly observations are 17%, -5 % , and 2%. Estimate the 5% VaR. X New Tab Sype for Balance f. x Concept- XBKM Ch 5..

Answer 1

The working and calculations for mean (expected rate of return), standard deviation, VaR and 5% Var are explained in the attached spreadsheet. The spreadsheet is self-explanatory. The answers to both parts of the questions are given in the spreadsheet.

ANSWERS TO a) of the Question PERIOD OF HOLDING GIVEN IN THE QUESTION 1 YEAR Absolute Expected Annual End of Year Value Annual Dividend Return in $ Return of Expected Annual Return of scenario Current Value of Variance of Portfolio in $ Scenario Business Condition в Probability in $ million million in $ million million scenario Return G E+F-D H=G/D J= ((H-ER)^2) C |=H X C A С D F High Growth Normal Growth 35 0.049 16.4 1 0.3 23 4.4 71.30% 21.39% 2 0.45 23 27 4 8 34.78% 15.65% 0.001 0.046 3 No Growth 0.2 23 15 -4 -17.39% -3.48% Recession 2.83% 30.74% -56.52% 4 0.05 23 8 2 -13 0.038 EXPECTED RETURN HOLDING PERIOD RETURN (ER) is sum of expected return of all scenarios 0.135 VARIANCE OF THE PORTFOLIO is sum of variance of all scenarios STANDARD DEVIATION OF THE PORTFOLIO OVER HOLDING PERIOD is square root of variance calculated as above 36.67% Based on above calculations and variance covariance method to calculate VALUE AT RISK (VaR), it is equal to Portfolio X Std Deviation X Z value at 5% Var Z-score value at 5% VaR i e. at 95% confidence level 1.645 IN $ MILLION So 5% VaR 23 X 37% X 1.645 14.00 This means 95% of time, the portfolio shall not loose more than $ 14 million over the holding period. There is only 5% chance of such a loss in the holding period VaR of a portfolio with normally distributed returns with same mean and standard deviation as above shall be as follows In a portfolio with normally distributed returns, its standard deviation itself is VaR and its VaR at different confidence levels can be calculated by multiplying the same with Z-score value. E.g. calculations are given below. Z-score ValueStandard Deviation in $ Million Confidence level VaR Interpretation 99% of time no loss of more than $ 19.65 million 99% Very High 95% High 2.33 36.67% 0.8545 19.65 1.645 36.67% 0.6033 13.88 95% of time no loss of more than $ 13.88 million ANSWERS TO b) of the Question Worst of 36 months sample rates of return given are 17%, -5% and 2 %. 5% VaR is estimated as follows Worst rates Mean of the worst rates 17% -5% 2% 4.67% 11.24% Z-score ValueStandard Deviation This is average of worst rates This is Standard Deviation of worst rates and derived by Excel Formula by using function STDEV Standard Deviation Interpretation 99% of time no loss of more than 26.19% of the portfolio 95% of time no loss of more than 18.49% of the porffolio Confidence level VaR 99% Very High 95% High 11.24% 0.2619 2.33 1.645 11.24% 0.1849