Question

Question two. Whiz is a recent hire at a large international bank. He is currently working on rotation in the risk management group, where he has received several assignments. For his first assignment, Rooney is given a portfolio of different asset classes of investment for a client who is considering arn additional equity investment to diversify the current portfolio. The share under consideration is for The Bata Company 2/25/2011 2/24/2011 2/23/2011 2/22/2011 2/18/2011 2/17/2011 2/16/2011 2/15/2011 2/14/2011 2/11/2011 2/10/2011 64.31 63.88 63.91 63.76 64.55 64.55 63.4 63.19 63.14 63.57 63.54 2/9/2011 2/8/2011 2/7/2011 2/4/2011 2/3/2011 2/2/2011 2/1/2011 1/31/2011 1/28/2011 1/27/2011 63.15 62.87 62.52 62.56 62.57 62.86 63.05 62.85 62.21 62.7 The client is concerned about the downside risk of the investment and as such want Whiz to calculate the Value at Risk (VAR) for the stock. The only data available is the daily prices for the last month. The investment under consideration is K 5 million. Required: (T). Calculate the Mean return of the share price of the Bata stock. (11). Assuming the standard deviation estimated for the above stock is 0.68%, provide an estimation of the following using the Variance-Covariance method: a. The daily VAR at 5% level of significance. b. The monthly VAR at 5% level of significance. C. The annual VAR at 5% level of significance. Applicable Z value for 5% level is 1.65 (5 marks) (5 marks) (5 marks) II).Outline the key limitations of using delta normal method for estimation of VAR and propose one method which can overcome the limitations.

Answer 1

(I)

| % 198116 821 6587692404|573 2 ?00-0-0-0-0 000-0000 00-Q0 45561 5579 7155676275 622322222333336 00000000000000000000R 22300 1|2|3 4 5 6 7 8 9 0|1|2|34 5 6 7 8 9

We calculate daily return. For example for daily return on 28-01-2011= =(C3-C2)/C2 = -0.00781

Then, we average out the daily returns for the given time period = =AVERAGE(D3:D22) = 0.13%

Therefore, the mean return of the share price is 0.13%

(II)

a. We have, Investment amount = 5000000; Return =0.13%; daily standard deviation σ_daily = 0.68%; 5% level of significance = 1.65

[0.13%-(1.65 x 0.68%)] = -0.99%

Therefore, Var _daily = 5000000 x 0.99% = 49500.

b. monthly standard deviation σ_monthly = 0.68% x (20 is the number of trading days in a month)

V20

= 3.04%

VAR =5000000 x 1.65 x 3.04% = 250800

c.

annual standard deviation σ_annual= 0.68% x $\sqrt{250}$ (250 is the number of trading days in an year)

= 10.75%

VAR _annual= 5000000 x 1.65 x 10.75% = 886875

(II) The limitation of delta normal method is that

• it assumes normal distribution curve. But the stock prices following normal distribution curve may not be realistic. Off-market factors can increase price volatility, which results in the normal distribution curve out of sync with actual market movement.
• This method also assumes that all the securities are linear in the risk factors.

In order to address these limitations, we can use Monte Carlo Simulation method. This is the most sophisticated method and allows any distribution and non-linear securities.