Financial Risk Manager

Portfolio P&L / VAR 99% ; A valid measure?

2010-03-01T16:06:02-08:00

> I was wondering if the RAROC ratio or a simple YTD P&L / VAR 99% could be a valid performance measure to evaluate the amount of risk used by a trader to explain a certain portfolio return (YTD P&L).

The goal here is to be able to compare the P&L of 2 traders function of their VAR utilization.

thank you very much!

calculation of the interest and principal payments in a mortgage

2010-02-27T14:44:48-08:00

HI David

are there any formulas to compute the interest payment part and the principal payment part in any part (month,year)
of the payment’s?

what are your thought on the odds that it will be tested in the exam?

BLACK SCHOLES MODEL

2010-02-26T12:44:55-08:00

Hi David,

While I once again thank u and your team for enabling many aspirants including me to qualify the prestigious FRM examination, I request you to clarify the following which I encountered when I was brushing up Hull’s OFD.

I would like to refer page 294 example 13.6 of Hulls OFD 7th edition, which calculates the price of call and put using BSM for a stock option expiring 6 months with volatility 20% p.a. The solution in the book shows that the volatility of 20% p.a. is directly plugged into the BSM formula..
1. Is the volatility given in the exercise a daily volatiltiy or a 6m volatility or a annual volatility?
2. In any case, should volatility be appropriately scaled to time ( in this case 6 m) before plugging into BSM formula? My understanding is that in BSM, Dr of d1, ie. sigma X sqrt (T) does the job of scaling and similarly the second part of the numerator (r + 0.5sigma^2)T does that for the variance (ie, sigma^2 X T). Is my understading correct?
3. If the question statement explicitly mentions volatiltiy as 6m volatility, should one discard the time scaling factor in the Nr and Dr. of d1, as plugging in would lead to scaling the volatility and variance twice? (provided my understanding in s.no.2 is correct).

Thanks in anticipation.

Manoj Kumar Halan.

Dynamic Asset Allocation and constant portfolio volatility

2010-02-14T05:39:28-08:00

Hi all

I am thinking about developing an asset management approach which will have a dynamic asset allocation with the aim to hold the portfolio volatility constant (the client can define a target volatility for his portfolio). The approach will be implemented particularly with ETFs. Furthermore, the potential loss in the portfolio will be reported regularly to the clients. In addition, the potential loss has to be in accordance to the preceding ALM.

Concerning this matter, I would be very pleased if I could ask you some questions about the control and measurement of volatility:

1. Which data frequency would you use to measure the volatility (high-frequency / daily / weekly / monthly)? Why?
2. Which data window would you use (how many days, weeks or months) to calculate the portfolio volatiliity? Why?
3. Wich models would you use to make a forecast for the portfolio volatility? For example: would you prefer EWMA or a typ of the GARCH familiy?
4. How would you measure the potential loss in the portfolio? For example with VaR and CVaR? Do you know other models?
5. Do you know useful instruments to generate buy- or sell-signals for the VIX (in connection with volatility forecasting)?

Thanks a lot!!!

Best regards,
Fractal

Monte Carlo and GBM

2009-11-06T11:05:23-08:00

Hello David,

I don’t know if this is something you’ve already talked about but forgive me for my short memory.. If Monte Carlo simulation is driven by GBM process, and since GBM does not model fat tails, then what is the adjustment that needs to be made to make MCS model heavy tails? Is it by the use of GARCH(1,1)? But then if we use GARCH(1,1), wouldn’t it model mean-reversion which we don’t want for stock prices? Or better, do we use EWMA instead?

Thanks!

Lower Bound of Euopean Currency Put

2009-11-17T03:21:12-08:00

Hi David,

Fr 2003 FRM exam,
-Current USD/AUD rate is 0.6650
-USD riskfree rate is 1%
-AUD riskfree rate is 4.5%
What is the lower bound of a 5 mth European put option on the AUD with a strike price of 0.6880?

Answer:
Lower bound = Xe^(-USD rf x 5/12) - Se^(-AUDRF x 5/12)
Lower bound = 0.6880xEXP(-0.01*5/12) - 0.6650xEXP(-0.045*5/12) = 0.0325

My confusions:
1) Why it is different with p>= max(Ke ^ -rT - S0, 0)?
2) Could we adjust the strike price and then minus the current exchange rate? 0.6880exp(-(0.01-0.045)*5/12) - 0.665
3) Could we use strike exchange rate minus the calculate the forward exchange rate? 0.6880 - 0.6650 exp(-(0.01-0.045)*5/12)

Your advice, please.

Thanks
Learning

3 Step Binomial Model (2004 FRM exam)

2009-11-17T00:43:08-08:00

Hi David,

Question:
An option on a stock has a payoff equal to the square of the positive excess of the stock price over the exercise price at expiration only if the stock exhibits an annual growth rate of 15% or more every year. Given the following assumptions and using a 3-step binomial model and rounding to the nearest USD, which of the following would be the option’s price?
-Time to expiration is 3 years
-Current price is USD10
-The annual std deviation is 15%
-The risk free rate is 5% per annum
-The strike price is USD10
-Assume the stock pays no dividends

Asnswer: A USD7

u = EXP(sigma*sqrt(t)) = EXP(0.15*SQRT(1.0)) = 1.162———- “1” instead of “3” is used bcos it is annual std deviation???
d=EXP(-sigma*sqrt(t))=EXP(-0.15*1.0) =0.861
p= (EXP(r*t)-d) / (u-d) = (exp(0.05*1)-0.861) / (1.162-0.861) = 0.633

Until here, I think I still can follow. But, I have confusion on the following part.

Option price formula = f = exp(-r*t)[pfu +(1-p)fd]
But, answer continues as follow
Option price = exp(-r*t)*p^3*(current price*1.162^3 - strike price)^2 = 7.04

Your guidance, please

Thanks
Learning

Currency Var - How to solve

2009-11-16T05:38:52-08:00

Hi David,

i seemed 2 b 2 stressed out and am not able to reach to solution to this simple problem. Can you pls help

Bank has a cash position of 1M Euro. The Euro exchange rate is 0.95 USD/EUR. The one-day Euro exchange rate is normally distributed with mean 0.95 and standard deviation 0.01. Compute the one-day Value at Risk with 95% confidence (in dollars).

Choose one answer
a. 19,600
b. 15,675
c. 18,850
d. 21,650

Correct is 15,675

Rgds
Amit

expected loss

2009-11-14T09:22:02-08:00

Hi david can u explain how to solve this question WITH CALCULATION.

which of the following loans has the lowest credit risk?

Loan 1 year PD Loss given default Remaining term in months

A 1.99% 60% 3
B 0.90% 70% 9
C 1.00% 75% 6
D 0.75% 50% 12

Thanks.

2009 FRM Level 1 PRACTICE EXAM - Q 22

2009-11-15T07:48:34-08:00

Hi David,

I have some confusion in the way this question has been answered. It states that “Expected decline in supply should increase further term commodity price”

Though i can see that the reason is due to the escalated storage cost taking cost of carry higher and hence in Contango, i have a specific doubt in terms of convenience yield here.

If i know that supply for a product is going to decline i would find it ” MORE CONVENIENT” to hold the commodity now and release it rationally thus taking my convenience yield high..probably much higher that my Storage costs thus spinning marked in Backwardation.

Pls clarify if i am missing some point here as based on this logic i had marked B as the answer while the correct as suggested by GARP IS A.

Thanks and best rgds
Amit