Probability concept problem-session 2 Challenge problems 4.b & c

CFA Level I Quant
#1

Hi all,

I have a question regarding the probability concept. Please help. Thank you very much.

Below is the question in Probability concept problem-session 2 Challenge problems 4.b & c

A bond that matures in one year is priced at $950 today. You estimate that it has a 10% probability of default. If the bond defaults, you expect to recover $600. If it does not default, it will pay $1080 at maturity. The nominal 1-year risk-free rate is 7.5%

B. What is the expected payoff on the bond in one year?

Answer is 0.1(600) +0.9(1080)=1032

I look at this I do not know why they need to calculate the total probability. Anyone can explain it? What is payoff means? thanks.

C. What is th expected return on the bond?

Answer is 1032/950-1=0.0863

which is ending value/beginning value-1. Holding period returns right? Why the ending value is 1032? This get me more confused.

._.

Thanks.

mc

#2

look at the different branches where you have the price of the bond.you have a 10% probability of default, and if it defaults you get 600$. If it does not default (the other 90% of the time) you have 1080.

So what can you “expect” to get out of investing in the bond? 0.1 * 600 + 0.9 * 1080 == 1032.

That is EXPECTED VALUE. (or PAYOFF because VALUE for you is PAYOFF for someone else).

Now to Part 2.

You got 1032 (above) by investing in the bond.

you paid 950 for it.

So what is the return? 1032 / 950 -1 …