Actuarial Outpost > CAS BKM Ch. 11 Question 21
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#1
02-13-2019, 01:39 PM
 CinderKat1 CAS Join Date: Feb 2019 College: UW-Madison Posts: 2
BKM Ch. 11 Question 21

21. Investors expect the market rate of return in the coming year to be 12%. The T-bill rate is 4%.
Changing Fortunes Industries’ stock has a beta of .5. The market value of its outstanding equity
is \$100 million.
a. What is your best guess currently as to the expected rate of return on Changing Fortunes’
stock? You believe that the stock is fairly priced.
b. If the market return in the coming year actually turns out to be 10%, what is your best guess
as to the rate of return that will be earned on Changing Fortunes’ stock?
c. Suppose now that Changing Fortunes wins a major lawsuit during the year. The settlement is
\$5 million. Changing Fortunes’ stock return during the year turns out to be 10%. What is your
best guess as to the settlement the market previously expected Changing Fortunes to receive
from the lawsuit? (Continue to assume that the market return in the year turned out to be 10%.)
The magnitude of the settlement is the only unexpected firm-specific event during the year.

I get parts a. and b. but do not understand the solution for part c. which says the following:

Given a market return of 10%, you would forecast a return for Changing Fortunes of 7%. The actual return is 10%. Therefore, the surprise due to firm-specific factors is 10% – 7% = 3%, which we attribute to the settlement. Because the firm is initially worth \$100 million, the surprise amount of the settlement is 3% of \$100 million, or \$3 million, implying that the prior expectation for the settlement was only \$2 million.

How do they get that the 3 million implies prior expectation of 2M?

I am sure I am missing something obvious.
#2
02-13-2019, 01:42 PM
 CinderKat1 CAS Join Date: Feb 2019 College: UW-Madison Posts: 2

Ok - I finally get it - if the original earning % was 7% but turns out to be 10% then that is a 3% "Surprise". If the total settlement was 5M then the amount of the original settlement built into the 7% estimate must be 2M = 5M - 3M surprise.

Ugh - I stared at it too long
#3
02-14-2019, 07:08 AM
 sacklunch Member CAS Join Date: Apr 2018 Posts: 249

I also struggled with this one. The following is how I kept it straight:

The expected total return was 7% * 100m = 7m, which includes some loading for expected lawsuit settlement.
(1) expected total return = expected normal return + expected lawsuit settlement

The actual total return is 10% * 100m = 10m, which includes the 5m settlement.
(2) actual total return = actual normal return + 5m
(3) actual normal return = 5m

It makes most sense to break this down into abnormal returns.
(4) abnormal total return = actual total return - expected total return
(5) abnormal total return = 10m - 7m = 3m

We know the abnormal total return is the only unexpected event, so the 3m abnormal total return is entirely due to the settlement, and this also means actual normal return = expected normal return = 5m.

So, from (1) expected lawsuit settlement = expected total return - expected normal return = 7m - 5m = 2m.