Financial Risk Manager

Theoretical Futures price

2010-04-27T09:56:46-08:00

Hi David,

Please help me in solving this question.

Question:

Suppose that the CTD (cheapest to deliver) bond for a Treasury bond futures contract pays 10% semi annual coupons on January 1 and July 1. This CTD bond has a conversion factor of 1.1 and a quoted bond price of 100. Assume that it is now April 1 2009. Also assume that Treasury bond futures contract to be delivered 180 days from today, and the risk free rate of interest is 3%. Calculate the theoretical price for this T-bond futures contract.

I am stuck at solving till :Accrued interest of 2.5 (for 90days) +100 = 102.50 (dirty price)
How to proceed further?

If you can explain thru excel (not a complusion ), I will practice for different maturity dates.

Thanks in advance

srinivas

CHEBYSHEV’S INEQ

2010-07-07T09:16:44-08:00

Hi David,
Probability that a random variable is 5 deviations from mean in a NORMAL DISTRIBUTION is 0.1350% (as calculated from excel function, ie, 1-normsdist(5) ).
For any unknown distribution, applying Chebyshev’s inequality, prob. that the r.v. is 5 sigma from mean is LESS THAN OR EQUAL TO 1/25, which is 4%.
1) Does the prob. of k-sigma dev. in a normal distribution and that of any unknown dist. (applying Chebyshev’s ineq) vary significantly. Or am I making any mistakes in the above two calculations?
2) I have so far understood that Chebyshev’s inequality provides only a maximum boundary. Is my understanding correct?

Thanks in anticipation,
Halan Manoj Kumar.

Is there an errata source for the Quant questions

2010-06-25T12:00:28-08:00

Are there errata on the Quant questions for Gujurati adn the other practice questions for the other readings?

Standard Deviation Daily Vs. Monthly

2010-06-21T07:15:28-08:00

Hi community, I was wondering if you might help me with some Standard Deviation calcs. Apologies in advance if the questions are very basic. I’m slightly overwhelmed though very very interested by the subject. I am preparing a presentation where I’d like to incorporate some stats concepts.

OK, so, let’s say I have 2 versions of price movements of the same security. The first one is daily view and the second one is a monthly view. For the sake of this exercise, we will say the security increases in absolute % value by 1% everyday for 360 days straight,starting with 1% on day 1. That means, on day 1, the security is up by 1%, on day 2 it is now up by 2% (for a total of 3%), on day 3 it increases by 3% (for a total of 6%).... on day 360, it increases 360% (for a total of 64980%)

Assume also, every 30 days is a month. The monthly version therefore has 12 data points. That means, on period 1/end of month 1/day 30, the security is up by 1365%, on period 2, it increases by 1365% (for a total of 1830%)... on period 12, it increases 10365% (for a total of 64980%, same as daily). I lay all this out in Excel.

Ok, so now I calculate the standard deviation for both sets. I use the STDEV function which from numerous testing, it seems to work well. The first set of data yield me a standard deviation of approx 104% and the second set gives me approx 3245%.

The difference seems quite big. Am I missing something?

Next, I try to annualize the Std Devs calculated. I may be completely off the mark here, but the formula that I find generally is Monthly Std Dec times the square root of 12.

I fill that in with the calculated monthly std dev and I get approx 112.4 for Annualized Std Dev.

I then take the same formula but instead of square root of 12 (for 12 periods), I substituted for 360 in hopes of annualized the Daily Std Dev I had calculated. Here, I come up with approx 187.32 Annualized Std Dev. I’m not sure if this is an OK conversion of the formula… yet the point that bothers me still is that both Annualized Std Dev I’ve calculated are quite different.

I know this is a lot to ask, but if you wouldn’t mind, can you pls tell me
- whether my methods of calculating the Daily, Monthly and the 2 Annualized Std Devs are all correct? If not, pls correct me
- If my calcs are correct, how exactly should I be interpreting the results as they seem to paint different stories regarding the volatility of the security.

Pls feel free to PM me if you’d like. I’d be happy to get on the phone to understand all this if there’s too much to write. Thanks all in advance for your help.

Question 4.03c

2010-06-19T16:31:16-08:00

This question asks what is the probability of obtaining X of 6? The answer list X~N(8,16/25), the probability that Z<= -2.5=.0062. I am confused with the notation. The question says “Consider a random variable Z~N(8.16)”, which is different than the notation in the answer, and the answer is “Z”, versus “X” in the question. I also can’t follow how the answer is .0062. Can you please list the steps taken to endup with probability of X of 6 = .0062.

Thanks,

Dan

L1 Practice /Some queries

2010-05-14T17:25:47-08:00

Hi David,

I have some queries. Hope you /some expert on the Forum could check:

Q5. For solving the DV01, I used your solution for 5.2. Got two CPT PV one as shown by you and the other simply changing (shocking) the yield to 2.49%.

Q6 There is a typo error in the Variance calculations:
9%(120-92)^2 + 42%(100-92)^2+49%(80-92)^2 = 168

Q12: Is it assumption that the contract size is $ 100,000

Q16. Is it okay to use the Portfolio VAR = SQRT (VAR1^2 + VAR2^2 + 2VAR1*VAR2*correl const FORMULA?
I did not get the calculations for diversified VAR. Seems some typo.
I tried solving for Marginal VAR using 2 x 2 matrix but getting Standard dev as 9.08656 ( Portfolio Variance 82.5655) . Could you
show the calculations for Marginal and Comp VAR. Is is expected in Level1 to calculate MVAR /CompVAR?

Q17. I checked z values for 1 = 0.3413 and for 2 = 0.4772 and added them ( .8185) >> how did you get .0228 and .1587?

so far so good.

Thanks.

Linear regression

2010-05-08T09:43:47-08:00

Hi David,

As far as i know linear regression is linear in the parameters - i wonder
can u post the refernce to Gujarati that says that linear model is linear in the parameters( may or may not be linear in the variables)
Thanks

Multicollinearity

2010-04-27T09:56:04-08:00

Hi David,

If there is a relationship between the independent variables, but it is not linear relationship, is the model still contained multicollinearity ?

Thanks

Question on Duration

2010-04-25T09:39:24-08:00

Hi David,

Please help me in solving this question.

Q: The information in the table below is for a callable corporate bond traded in the secondary market. What will be the bond’s percentage price change if its yield declines by 0.50%?

Bond A

Coupon rate 8.30%
Price 101.56
Effective Duration 4.23
Yield Based DV 01 0.0445
Modified Duration 4.39
Macaulay Duration 4.56

The Answer is: 2.12% (how?)

(What is effective duration and when should we use this?)

Thanks in advance !!

Srinivas

formula

2010-04-25T08:28:49-08:00

Hi David

Kindly confirm as to are these formula same for the covariance same or different in some aspect

E(X-X)(y-y) & E(XY)-E(X)E(Y) as used on pg 29 & 27 of L1 study notes.

Thanks