Here’s a fun one. (CFAI Vol 5 p. 258) An analyst would like to know the VAR for a portfolio consisting of 2 asset classes: LT Gov’t bonds issued is the US and Gov’t bonds issued in the UK. The expected monthly return on US bonds is 0.85%, and the standard deviation is 3.2%. The expected monthly return on UK bonds in US dollars is 0.95% and the standard deviation is 5.26%. The correlation between the US dollar returns of UK and US bonds is 0.35. The portfolio MV is $100 million and is equally weighted between the 2 asset classes. Using the analytical or variance-covariance method, compute the following: I. 5% Monthly VAR II. 1% Monthly VAR III. 5% Weekly VAR IV. 1% Weekly VAR
got this to look forward to next week… awesome. i’m almost to the equity end of chap questions… at least it’s going faster than the ips and asset allocation probs.
Rock on cfasf. I’ve gone through a full 100 page notebook (both sides) in the past 2 weeks writing out these damn ?'s. Clicking through Q-bank for L1 and L2 was much less time consuming.
I. 6.008 million II. 8.18 million III. 3.23 million IV. 4.31 million Good exercise for VAR calculations.
I believe you’re missing something. What are your inputs?
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step 1. Calculate the monthly return and standard deviation for the portfolio step 2. Calculate the 5% monthly VAR as = return - 1.96*(stdev) for the portfolio step 3. Calculate the 1% monthly VAR as = return - 2.576*(stdev) for the portfolio step 4. calculate the weekly return as monthly return/4 step 5. calculate the weejly stdev as monthly stdev/2 step 6. do step 2 and 3 for weekly VAR Please let me know if there is some error as i got the figures mentioned by me above. I checked one website which said that we need to take 1.65 and 2.33 stdev for 5% and 1%, following are the results using these figures. I.3.8 million II. 6.18 million III. 2.4 million IV. 3.6 million Please let me know if I am missing something. Thanks.
Yeah, we need to use 1.65 and 2.33 because we’re only concerned with the lower end of the distribution. Steps 2 - 3: Process is correct (substitute 1.65 and 2.33) I think your portfolio standard deviation might be off 'cuz the monthly VAR is still coming up short. Steps 4 - 5: To get the weekly return and stdev, we actually have to take it out to one year first, and then back down to weekly figures (stdev monthly * (12^1/2) / (52^1/2)
Thanks a lot McLeod, appreciate ur help and suggestion. Look forward towards working together and getting over this monster this June
dont forget that the st dev for the portfolio is not just simply weighted, but instead the markowitz method.
rekooh Wrote: ------------------------------------------------------- > dont forget that the st dev for the portfolio is > not just simply weighted, but instead the > markowitz method. what’s that?
i can’t type it, becuase i don’t have subscript but essentally weight of security A squared *variance of A + weight of security B squared *variance of B + 2 * weight of A * weight of B * covariance A,B with covariance A,B equalling corr A,B*st dev A*st dev B
Oh, i see what you mean. You suggest using the correct formula for the standard deviation of the weighted sum of two assets.
exactly. If you don’t use the weighted deviations and interplay of the covariance then the SD will be wrong
can you provide more details on the calculation of this? I think i have the right method but not coming to the answer. Thanks
Expected Return: 0.5*0.85 + 0.5*0.95 = 0.90% (Monthly Return) Std Dev = [(0.5)^2*(3.2)^2 + (0.5)^2*(5.26)^2 + 2*0.5*0.5*3.2*5.26*.335]^1/2 = 3.525% (Monthly Std) 5 Month VAR = [0.0090 - .03525*1.65]*100 mn = -4,916,250 1 Month VAR = [0.0090 - .03525*2.33]*100 mn= 7,313,25 Same Formula for monthly calculation except substitute 0.90 return with (0.0090*12/52) = 0.00207% for Weekly Return AND 0.03525% Std Dev with (.03525*(12)^1/2)/(52^1/2) = 0.01693% for Weekly Std. Dev