Transcript Document

Test 2
Spring 2014, 10 am Class
Multiple Choice #1
Three stocks have annual returns of 8%, 12%,
and 16%. The variance of this sample is
.𝟎𝟖+.𝟏𝟐+.𝟏𝟔
Average =
=. 𝟏𝟐
𝟑
𝟏
Variance = [ . 𝟎𝟖−. 𝟏𝟐 𝟐 +
𝟐
𝟐
. 𝟏𝟐−. 𝟏𝟐
+ . 𝟏𝟔−. 𝟏𝟐 ] =. 𝟎𝟎𝟏𝟔
𝟐
Multiple Choice #2
Amy invested $1 in a company 50 years ago. This
investment is worth $60 today. What is the
geometric average annual return on this
investment?
Geometric Average =
𝟓𝟎
𝟔𝟎 − 𝟏 =. 𝟎𝟖𝟓𝟑𝟑𝟑
Multiple Choice #3
Assume that the risk-free return in the market is
currently 6%, and that a stock with 𝛽 of 2.5 has
an expected return of 11%. What is the
expected return on the market portfolio (as
defined in lecture)?
𝑬 𝑹𝑺 = 𝑹𝒇 + 𝜷 𝑬 𝑹𝑴 − 𝑹𝒇
. 𝟏𝟏 =. 𝟎𝟔 + 𝟐. 𝟓 𝑬 𝑹𝑴 −. 𝟎𝟔
⟹ 𝑬 𝑹𝑴 =. 𝟎𝟖
Multiple Choice #4
Bo’s Buckwheat and Barley, Inc. has issued a bond with 10
remaining coupon payments of $100 each. The first will
be paid in 3 months, and each subsequent payment will
be made annually. The bond also pays out a face value of
$750 with the last coupon payment. If the effective
annual discount rate is 8%, what is the present value of
the bond?
𝟏𝟎𝟎
𝟏
𝟕𝟓𝟎
𝑷𝑽 =
x
𝟏−
+
𝟏𝟎
. 𝟎𝟖
𝟏. 𝟎𝟖
𝟏. 𝟎𝟖𝟗.𝟐𝟓
= $𝟏, 𝟎𝟕𝟖. 𝟗𝟐
𝟑
𝟏. 𝟎𝟖𝟒
Multiple Choice #5
Stock Q has an expected return of 8% and a
variance of .04. Stock Z has an expected return
of 14% and a variance of .09. The correlation is
strictly greater than -1 and strictly less than 1.
Which of the following – 8%, 16%, 24% 32% –
could NOT be the standard deviation at the
minimum variance point of a portfolio consisting
of Stock A and/or B?
Multiple Choice #5
Since 𝜌 ≠ 1, the minimum standard deviation of
a portfolio mixing the two stocks must be below
the standard deviation of both stocks.
𝝈𝑸 = . 𝟎𝟒 =. 𝟐
𝝈𝒁 = . 𝟎𝟗 =.3
Neither 24% nor 30% can be a minimum.
Free Response #6
Charlotte buys a stock that pays a dividend of $5 today
(May 28, 2014), followed by annual dividends on the
same date each year forever. The dividends grow by 5%
each year until 2020 and then remain constant forever.
If the effective annual discount rate is 20%, what is the
present value of the stock?
𝟓
𝟏. 𝟎𝟓
𝑷𝑽 =
𝟏−
. 𝟐−. 𝟎𝟓
𝟏. 𝟐
= $𝟑𝟓. 𝟓𝟏
𝟔
𝟓 𝟏. 𝟎𝟓
x 𝟏. 𝟐 +
.𝟐
𝟔
𝟏
x
𝟏. 𝟐𝟓
Free Response #7
• A zero-coupon bond is purchased for $800 at 10
am today, with a face value of $1,000 to be paid 3
years from today. Later today, at 1 pm, the yield
to maturity (as an effective annual rate) changes
to 9%. How much does the value of the bond
change between 10 am and 1 pm?
$𝟏,𝟎𝟎𝟎
𝟏.𝟎𝟗𝟑
Value at 1 pm:
= $𝟕𝟕𝟐. 𝟏𝟖
The value decreases by $𝟖𝟎𝟎 − $𝟕𝟕𝟐. 𝟏𝟖 =
$𝟐𝟕. 𝟖𝟐
Free Response #8
A sample of a stock’s returns over the past 5
years was 200%, 50%, -40%, 20%, and -10%. If
the stock is worth $200 per share today, how
much would each share have been worth 5
years ago?
𝑿 𝟏 + 𝟐 𝟏+. 𝟓 𝟏−. 𝟒 𝟏+. 𝟐 𝟏−. 𝟏
= $𝟐𝟎𝟎
𝑿 = $𝟔𝟖. 𝟓𝟗