Tennessee National Bank has a stock portfolio with a market value of $40 million

Question

Tennessee National Bank has a stock portfolio with a market value of $40 million. The beta of the portfolio is beta = 1.25; whereas, the market portfolio beta is 1.0 (beta = 1). The market portfolio's daily standard deviation (sigma_m) is estimated at 1.6 percent (.016). What is the DEAR and 5-day VAR of this portfolio, using adverse rate changes in the 99^th percentile, which is also the 98 percent confidence interval (Z_alpha/2=2.33)? DEAR = ($ Value of portfolio) times (Z_alpha/2 times beta times sigma_m)

Explanation / Answer

Given : Beta of portfolio=B=1.25 Std Dev of Market Portfolio=1.6% 98% confidence Interval=Z(/2)=2.33 $ value of Portfolio=40 Million DEAR =($value potfolio)*Z(/2)*Beta*Std Dev of Market portfolio =40,000,000*2.33*1.25*0.016=                   1,864,000 So DEAR =$1,864,000 VAR = DEAR /Sq Root of N Where N = no of days Here N =5 So VAR for 5 days= 1864000/Sq Rt 5=1864000/2.2361=                       833,594 So Required VAR =$833,594

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