**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%**
**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%**
**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.**
**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 not 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**.
**Bond Value, Current Yield**
Bond-1 Bond-2
Face Value 100 100
Annual Coupon 8% 10%
Term to Maturity 3 yrs 4 yrs
Market Price 80 90
**Ex. 1 **Find Current Yield of Bond 2
Solution
Coupon amount X100 = 10/90*100 = 11.11%
Market Value
**Ex. 2 **Find YTM of Bond 1 & 2
YTM of Bond 1 = 17.07%
YTM of Bond 2 = 13.41%
**Ex. 3 **Find McCauley Duration of Bond 1
2.76 years
**Ex. 4**
Find Modified Duration of Bond 2
Solution
McCauley duration/1+yield
=3.46/(1+13.41%) = 3.46/1.1341 = 3.05 yrs.
**Ex. 5 **What is %age change in price of Bond 2 if YTM increases by 1%
Expected %age change in price
=Modified Duration x %age change in yield
=3.5 x 1 = -3.05% (Decrease in price of bond)
**Ex. 5 **What is %age change in price of Bond 2 if YTM decreases by 1%
=3.5 x 1 = 3.05% (Increase in price of bond)
**Ex.6 **As an investor, in which bond would you like to invest.
Bond 1 (YTM is more)
**AMA – Estimated level of Operational Risk and Impact of Internal Control**
**Question: **Probability of Occurrence : 4
Potential Financial impact =4
Impact of Internal controls = 0%
**Solution:**
{ Probability of occurrence x Potential financial impact x Impact of internal controls } ^0.5
=(4x4) ^0.5 = ∫16 = **4 Ans**.(**High Risk**)
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