Q&A bank, question 5.15.iii

[fisherbobby]

The solution to this question has the duration of the porfolio A + B calculated as the average of the durations of the two assets A and B.

However in the text the duration of a portfolio of more than 1 asset is defined as the discounted mean term weighted by present value for all the cashflows for all assets.

For example, in 5.15 we have:

DMT(A) = 400/88.77 = 4.51

DMT(B) = (100*22*1.08^-22)/(100*1.08^-22) = 22

the average is 13.25, which is the solution given in the Q&A bank.

If we had calulated the DMT as per the text we would have:

DMT = (400+100*22*1.08^-22)/(88.77+100*1.08^-22) = 7.5

The solution to the Q&A bank is putting equal weight to both DMT(A) and DMT(B) whereas the value of asset A is much larger than asset B, 88.77 compared to 18.39. I believe the two individual durations should have been weighted by present value, rather than by amount. Am I missing something?

Cheers

 

[John Lee]

The solution to this question has the duration of the porfolio A + B calculated as the average of the durations of the two assets A and B.

However in the text the duration of a portfolio of more than 1 asset is defined as the discounted mean term weighted by present value for all the cashflows for all assets.

For example, in 5.15 we have:

DMT(A) = 400/88.77 = 4.51

DMT(B) = (100*22*1.08^-22)/(100*1.08^-22) = 22

the average is 13.25, which is the solution given in the Q&A bank.

If we had calulated the DMT as per the text we would have:

DMT = (400+100*22*1.08^-22)/(88.77+100*1.08^-22) = 7.5

The solution to the Q&A bank is putting equal weight to both DMT(A) and DMT(B) whereas the value of asset A is much larger than asset B, 88.77 compared to 18.39. I believe the two individual durations should have been weighted by present value, rather than by amount. Am I missing something?

Cheers

You are answering the question as if you were purchasing £100 nominal of each of A and B.

However, the question says you invest equal amounts in A and B, ie you have the same PV of each of A and B.

 

[fisherbobby]

I don't have the notes with me but I think the same wording, invest, is used throughout the text to mean the amount of a particular asset that is bought. The notes usually mention value when refering to present values and amounts when they refer to nominal.

I do not have an economics/finance background, but I didn't feel that I struggled too much with the rest of the text so it is a surprise that this particular exercise would be refering to the present value of assets A and B rather than the amount that was bought. This question would be impossible to solve if it were refering to amounts.

 

[John Lee]

I don't have the notes with me but I think the same wording, invest, is used throughout the text to mean the amount of a particular asset that is bought. The notes usually mention value when refering to present values and amounts when they refer to nominal.

I do not have an economics/finance background, but I didn't feel that I struggled too much with the rest of the text so it is a surprise that this particular exercise would be refering to the present value of assets A and B rather than the amount that was bought. This question would be impossible to solve if it were refering to amounts.

Invest has been used in the exam to mean the amount to purchase an asset. If it wants the nominal it will be very clear.

 

[fisherbobby]

yes, I agree with you, thanks for helping.

 

[johnpe21]

so we can't solve those exercises, and in particular this one, using the nominal value and then discount it to find the present value?

Would it be wrong to say:

DMTa=PU^5 + (0,05PU+0,05P(1+g)U^2+...+0,05P(1+g)^4U^5) ?

 

[John Lee]

so we can't solve those exercises, and in particular this one, using the nominal value and then discount it to find the present value?

It's totally fine to do it that way.

 

[johnpe21]

thank you very much for the replies !