Module 3 section 4 Investment Science

[frisbbzepp]

I'm having trouble with the questions from chapter 3 of the book. Anyone want to compare solutions?

I also got a little confused on slide 17, the one where you calculate duration for a bond. The yield is given as 6%, and in the solution that rate is used. However, in the text, it seems that the yields given are always assumed to be compounded semiannually, so when I did the problem, I used 3%. Anyone else finding this a little weird?

[weinerda]

I don't have my book with me, but I believe if you assume a compounding frequency that is the same as the coupon payment frequency you should match the solutions. Also, whatever they give you on the spreadsheet for timing is, I believe, what you should use (i.e. if they give you space for semiannual cashflows, then the compounding frequency is semiannual) Hope this helps.

[frisbbzepp]

I think they do give space for semiannual cashflows (i.e. times 0.5, 1, etc.) but then they still use the yield as given. That's why I was confused.

[weinerda]

Oh. I don't remember that happening... oh well... At least you figured it out.

[frisbbzepp]

I thought the life expectancy question was going to be easy, but I couldn't get the book. I just tried to calculate the sum of , but no dice.

[weinerda]

Originally Posted by frisbbzepp

I thought the life expectancy question was going to be easy, but I couldn't get the book. I just tried to calculate the sum of , but no dice.

Haha... I did the same thing... except the problem was geared towards non-actuaries... the probabilities given are really 1|Qx . You'll see they sum to 100%. (The life expectancy is just the sumproduct of the probabilities times the ages.)

[frisbbzepp]

What's the theory behind that? How do they end up being equivalent? But thanks for the explanation, I'm glad I just wasn't going crazy. How can you use that information to get part (c). I was trying to do and it wasn't working out.

[weinerda]

You have to think simpler... Only an actuary (and one who has taken MLC) would do what you (and I) did. Just find the value of the annuity if Mr. Jones dies at each age, and sumproduct with the probabilities as before.

By the way, I found some of the theoretical chapter questions (they come later) to be rather difficult... I think what's important here is the concepts, which you clearly understand even better than the average reader.

Oh, and as to how they are equivalent, if you use the fact that the probabilities are 1|qx and convert them to tpx and sum then you can reconcile exactly. It can get a little messy, but you have to use the relation that t|qx = tpx * qx+t to back out the p's.

[frisbbzepp]

Did you understand the convexity spreadsheet? I got the first way they did it, but I thought the one with the formula that was something like second difference in price (which was never defined in the text) over the product of change in yield squared and central price was weird. Never would have used that if they hadn't spelled it out.

[weinerda]

Originally Posted by frisbbzepp

Did you understand the convexity spreadsheet? I got the first way they did it, but I thought the one with the formula that was something like second difference in price (which was never defined in the text) over the product of change in yield squared and central price was weird. Never would have used that if they hadn't spelled it out.

Short answer: "No." I didn't really dig into how they came up with that... I sort of just guessed that it had to do with the definition of derivative as:

Lim as h->0 of: [f(x+h)-f(x)]/h

which is a difference of sorts... Convexity is a second derivative... sooo... second difference. In practice I would probably use the former method, so like I said, I didn't spend too much time trying to derive it.