Numericals for Risk management

 Volatility with time horizon & Bond Value 

Ex.1 
If daily volatility of a Security is 2%, how much will be monthly volatility? 
Solution 
Monthly volatility = Daily Volatility * ∫30 = 2*∫30 = 2*5.477 = 10.95% Ans 
Ex.2 
If per annum volatility is 30% and nos. of trading days per annum be 250, how much will be 
daily volatility? 
Solution 
Annual Volatility = Daily Volatility * ∫250 = Daily Volatility * 15.81 
30 = Daily Volatility *15.81 
Daily volatility = 30/15.81 = 1.90% Ans. Ex.3 
If 1 day VaR of a portfolio is Rs. 50000/- with 97% confidence level. In a period of 1 year of 
300 trading days, how many times the loss on the portfolio may exceed Rs. 50000/-. Solution 
97% confidence level means loss may exceed the given level (50000)on 3 days out of 
100. 
If out of 100 days loss exceeds the given level on days =3 
Then out of 300 days, loss exceeds the given level = 3/100*300 =9 days. Ans. Ex.4 
A 5 year 5% Bond has a BPV of Rs. 50/-, how much the bond will gain or lose due to 
increase in the yield of bond by 2 bps 
Solution 
Increase in yield will affect the bond adversely and the bond will lose. Since BPV of the bond is Rs. 50/-. Increase in yield by 2 bps will result into loss of value 
of Bond by 50*2=100. Ex.5 
1 day VaR of a portfolio is Rs. 50000/- with 90% confidence level. In a period of 1 year (250 
days) how many times the loss on the portfolio may exceed Rs.50000/- Ans. 90% confidence level means on 10 days out of 100, the loss will be more than Rs. 50000/-. Out of 250 days, loss will be more than 50000/- on 25 days Ans. It means, out of 250 
days, loss will not exceed on 225 days.