Swap maximum potential exposure

[Bester]

Hi,

Can you please assist in explaining why the duration of the bond is 7 years I.e. (10)0.5] and why the answer multiplies by 3.16?

Is this also a type of question we can expect in the exam?


Question:

Hong Kong Shanghi Bank has entered into a repurchase agreement with a client where the client will sell a 10-year US treasury bond to the bank and repurchase it in 10 days. The bond has a notional value of USD 10m, trades at par with the yield volatility for a 10-year US treasury 0.074%. The swap's maximum potential exposure at a 99% confidence level is closest to:

a. USD 320,000 b. USD 380,000 c. USD 550,000 d. USD 1,200,000

CORRECT: B

The approximate duration for a 10 year bond is 7.0. The volatility of the swap value over 10 years is calculated as follows: σ(V) = [market_value * duration * yield volatility *(10)0.5] = 10,000,000 * 7.0 * 0.00074 * 3.16 = 163,806.

To get the 99% confidence interval, we multiply σ(V) by 2.33, which gives approximately $380,000.

 

[ShaktiRathore]

I dont know abt the Duration,
The 1 day volatility is, σ(V) = [market_value * duration * yield volatility ] = 10,000,000 * 7.0 * 0.00074
Its just scaled by sqrt(10)=10^.5=3.16 to get volatility over 10 days as σ(V) = [market_value * duration * yield volatility *(10)^0.5] = 10,000,000 * 7.0 * 0.00074 *3.16
Multiply this with 2.33 to get 99% potential exposure.
Yes such questions can come.
Thanks

 

[Bester]

Thanks, I did not realize that the volatility in the question is expressed as daily. Therefore agree that the 10 day volatility is sqrt(10) multiply by 0.00074. Also not sure how duration is 7 years? I would have used 10 years as no ytm is given to convert to modified duration.

 

[ShaktiRathore]

I think its standard US treasury bond would have fixed yield and term implying an approximate duratiin could be obtained by multiplying term of 10 yrs with a fixed factor.
Thanks

 

[Bester]

Hi,

Here is another question where it is unclear for me how the duration was obtained for the 6% bond. I assume we will not be asked this type of question in the exam, if the duration is calculated by multiplying term with fixed factor, else I don't now how to calculate the duration for the 6% bond. In this example again I would have assumed the duration is equal to modified duration, thus using the ytm to calculate the modified duration.

Question

What is the best estimate of the market value of a portfolio of USD 100 million invested in recently issued 6% 10-year bonds and USD 100 million of long 10-year zero coupon bond if interest rates decline by 0.50%:

a. USD 219 million b. USD 195 million c. USD 209 million d. USD 206 million

ANSWER: C To calculate the best estimate of the market value of the portfolio if interest rates decline 0.5%, one needs to calculate the change in the market value of each bond using duration. The duration of the 10-year zero coupon bond is 10. Thus, the change in value of this bond equals 10x0.005x100,000,000, which equals 5 million dollars.

The duration of the newly issued 6% bond is 7.802 assuming that the price of the bond is par. Given a duration of 7.802, the change in the value of the bond equals 7.802x0.005x100,000,000 which equals 3.91 million.

Thus, the best estimate of the market value of the portfolio if interest rates decline by 0.5% is 200 million + 5 million + 3.91 million which equals 208.91 million. Thus, the correct answer is ‘C'.

 

[ShaktiRathore]

Hi
Yes these type of questions shall not appear in the exam where its unclear what the input like duration is,evrrything required for the question to be solved would be explicitely mentioned in the exam,i have not seen such type of questions where its unclear about some inputs, every input required to solve the question would be in the question othetwise how would you do it. The above questions where its unclear from where the duration is coming from makes the question bizzare which is highly unlikely in the exam. I think questions as above should have clearly given inputs to find duratiin or would have mentioned the duration in qiestion itself to be like exam type,certainly above questions do not appear as such in exam where inputs are not obtainable.
Thanks

 

[Bester]

Thanks

 

[David Harper CFA FRM]

@ShaktiRathore is correct, as usual. Old questions do tend to require an assumption about duration, but that was many years ago when frankly the syllabus was much simpler. Bank then it was common to assume a 7.0 year duration for a 10-year coupon bond, as a rough approximation; but GARP will definitely not do this in the "modern" FRM as the syllabus is obviously more sophisticated. So the OP question above (Hong Kong Shanghi Bank) would simply not be asked, including the reference to "maximum potential exposure" as this preceded the Counterpary credit terms and is suggestive of those terms (e.g., PFE, max PFE); today, the question would simply ask VaR.

The second question, also, would never been seen because you can't just assume the bonds are priced at par per "The duration of the newly issued 6% bond is 7.802 assuming that the price of the bond is par." Now, if the question told you the coupon bond was priced at par, we do have the analytical solution: under an assumption of annual coupons, if c = y such that bond prices at par, then Macaulay duration = (1+y)/y * [1-(1+y)^-T] = 1.06/0.06 * (1-1.06^-10) = 7.802, which is an annual variation on Tuckman's formula 4.45, but to my knowledge it is not strictly assigned. Thanks,