ch,12 Flashcards
You bought a bond for $950 1 year ago. You have received two coupons of $30 each. You can sell the bond for $975 today.What is your total dollar return?
Income = $30 + $30 = $60
Capital gain = $975 – $950 = $25
Total dollar return = $60 + $25 = $85
You bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40.
What is your dollar return?
What is your percentage return?
Dollar return = $1.25 + ($40 – $35) = $6.25
Dividend yield = $1.25/$35 = 3.57%
Capital gains yield = ($40 – $35)/$35 = 14.29%
Total percentage return = 3.57% + 14.29% = 17.86%
What is risk premium
The risk premium is the return over and above the risk-free rate.
risk premium is the investment return an asset is expected to yield in excess of the risk-free rate of return.
Variance and standard deviation measure
the volatility of asset returns.
The greater the volatility, the ________
greater the uncertainty
You invested $100 in a stock five years ago. Over the last five years, annual returns have been 15%, –8%, 12%, 18% and –11%.
1. What is your average annual rate of return?
2. What is your investment worth today?
- What equivalent rate of return (geometric average) would you have to earn every year on average to achieve this same future wealth?
- average arithmetic: “ 5.2”
- FV = $100(1+0.15)(1– 0.08)(1+0.12)(1+0.18)(1– 0.11) = $124.4
- average geometric: 4.47%
*look at slide 22
Efficient markets _________ imply that investors cannot earn a positive return in the stock market.
DO NOT
What makes markets efficient?
There are many investors out there doing research
- As new information comes to market, this information is analyzed and trades are made based on this information.
- Therefore, prices should reflect all available public information.
If investors stop researching stocks, then the market will not be efficient.
Common Misconceptions about EMH
(efficient market hypothesis)
Efficient markets do not mean that you can’t make money.
They do mean that, on average, you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns.
Market efficiency will not protect you from wrong choices if you do not diversify - you still don’t want to put all your eggs in one basket.
Strong form efficiency
Prices reflect all information, including public and private.
If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed.
Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns.
Semistrong Form Efficiency
Prices reflect all publicly available information including trading information, annual reports, press releases, etc.
If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information.
Implies that fundamental analysis will not lead to abnormal returns.
Weak form efficiency
Prices reflect all past market information such as price and volume.
If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information.
Implies that technical analysis will not lead to abnormal returns.
Empirical evidence indicates that markets are generally weak form efficient.
Risky assets earn _________
a risk premium.
In an efficient market ______________
prices adjust quickly and correctly to new information
You purchased a stock for $47.00 a share one year ago. Today you sold the
stock for $50.21 a share and realized an 8.51% total rate of return. What was
the dividend yield on this stock for the past year?
The capital gain yield is given by ($50.21 − $47.00)/$47.00 = 6.83%. Hence,
the dividend yield is 8.51% − 6.83% = 1.68%.
A year ago, you purchased 300 shares of IXC Technologies, Inc. stock at a
price of $9.03 per share. The stock pays an annual dividend of $0.10 per share.
Today, you sold all of your shares for $28.14 per share. What is your total
dollar return on this investment?
Total dividend dollar return is $0.10 × 300 = $30.
Total capital gain dollar return is ($28.14 − $9.03) × 300 = $5, 733.
Therefore, total dollar return is $30 + $5, 733 = $5, 763.
You just sold 200 shares of Langley, Inc. stock at a price of $38.75 a share.
Last year you paid $41.50 a share to buy this stock. Over the course of the
year, you received dividends totaling $1.64 per share. What is your capital gain
on this investment?
Capital gain portion of the investment does not count dividends paid into
consideration. It is simply given by ($38.75 − $41.50) × 200 = −$550.
- Suppose a stock had an initial price of $79 per share, paid a dividend of
$1.45 per share during the year, and had an ending share price of $88.
Compute the percentage total return.
Total dollar return per share is ($88 − $79) + $1.45 = $10.45. Therefore, the
percentage total return is $10.45/$79 = 13.23%.
- Suppose a stock had an initial price of $79 per share, paid a dividend of
$1.45 per share during the year, and had an ending share price of $88.
. In Problem 1, what was the dividend yield? The capital gains yield?
The dividend yield was $1.45/$79 = 1.84%. The capital gains yield is
($88 − $79)/$79 = 11.39%. Alternatively, the capital gains yield is
13.23% − 1.84% = 11.39% as the sum of the dividend yield and the captial
gains yield is the percentage total return.
- Suppose you bought a 7% coupon bond one year ago for $970. The bond
sells for $940 today.
a. Assuming a $1,000 face value, what was your total dollar return on this
investment over the past year?
b. What was your total nominal rate of return on this investment over the past
year?
c. If the inflation rate last year was 3%, what was your total real rate of return
on this investment?
a. Total dollar return = Changes in the price + Coupon =
($940 − $970) + $1, 000 × 7% = $40.
b. The total percentage return (nominal rate of return) is $40/$970 = 4.12%.
c. Recall the Fisher equation from Chapter 7: (1 + R) = (1 + r)(1 + h) where
we have R = 4.12% and h = 3%. Then, we have
r = 1+R
1+h − 1 = 1+0.0412
1+0.03 − 1 = 1.09%.
Using the following returns, calculate the arithmetic average returns, the
variances, and the standard deviations for X and Y.
Returns
Year X Y
1 15% 21%
2 26% 36%
3 7% 13%
4 -13% -26%
5 11% 15%
σ(X) =
√
0.02042 = 14.29%.
σ(Y ) =
√
0.05277 = 22.97%.
*qs 7 tutorial
- You’ve observed the following returns on Regina Computer’s stock over the
past five years: 7%, -12%, 11%, 38%, and 14%.
a. What was the arithmetic average return on Regina’s stock over this five-year
period?
b. What was the variance of Regina’s returns over this period? The standard
deviation?
a. 11.60%.
b. the standard deviation σ(R) =
√0.03203 = 17.89%.
*qs 9 turotial
- You bought one of Glenelm Co.’s 6.5% coupon bonds one year ago for
$1,090. These bonds make annual payments and mature in 14 years from now.
Suppose you decide to sell your bonds today when the required return on the
bonds is 5.2%. If the inflation rate was 3.9% over the past year, what was your
total real return on investment?
PV= $1, 127.05.
Then, the nominal total percentage return can be computed as
R = [($1, 127.05 − $1, 090) + $65]/$1, 090 = 9.36%.
r=5.26%
- You find a certain stock that had returns of 9%, -16%, 21%, and 17% for
four of the last five years. If the average return of the stock over this period
was 10.3%, what was the stock’s return for the missing year? What is the
standard deviation of the stock’s return
R = 20.5%.
σ =√0.02392 = 15.47%.
