Risk and Return chapter of financial mangement

This is about the risk and return calculation.

2. Investment returns measure the
financial results of an investment.
Returns may be historical or
prospective (anticipated).
Returns can be expressed in:
Dollar terms.
Percentage terms.

3. Dollar return:
Percentage return:
$ Received - $ Invested
$1,100 - $1,000 = $100.
$ Return/$ Invested
$100/$1,000 = 0.10 = 10%.

4. Income received on an investment plus any Income received on an investment plus any
change in market price, usually expressed as change in market price, usually expressed as
a percentage of the beginning market price a percentage of the beginning market price
of the investment.of the investment.

5. Dt = the periodic cash flows
The cashflows of stocks are dividends
The cash flows of bonds are the periodic int
payments
Pt = price at the end of period
Pt-1 = price at the beg of period

6. Total return = Yield + Capital gains

7. Example:
You buy a stock for $100 (beginning price)
It pays $5 dividend (income)
Its price rises to $110 (ending price)
Total Return=?

8. Example: Assume the purchase of a 10-percent-
coupon Treasury bond at a price of $960, held
one year, and sold for $1,020. The TR is ?

9. Typically, investment returns are not known
with certainty.
Investment risk pertains to the probability of
earning a return less than that expected.
The variability of returns from those that are
expected.
The greater the chance of a return far below
the expected return, the greater the risk.

10. A set of possible values that a random
variable can assume and their associated
probabilities of occurrence.
Helps in calculating Expected Return
◦The weighted average of possible returns, with
the weights being the probabilities of occurrence.

11. Based on historical data
◦Observe past data
◦Count how often each return occurs
◦The frequencies becomes our returns
Based on economic scenarios
◦When future data isn’t known
◦Chose probabilities based on economic trends
Economic models
Note: In finance the most common method is
Based on historical data.

12. Suppose a stock had these annual returns over
10 years:
3 years: loss of 5%
5 years: gain of 10%
2 years: gain of 20%
Return Frequency Probability
–5% 3/10 = 0.3 30%
10% 5/10 = 0.5 50%
20% 2/10 = 0.2 20%

13. Economy Prob.T-BillHT
stocks
Coll US MP
Recession 0.10 8.0%-22.0% 28.0% 10.0%-13.0%
Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0
Average 0.40 8.0 20.0 0.0 7.0 15.0
Above avg. 0.20 8.0 35.0-10.0 45.0 29.0
Boom 0.10 8.0 50.0-20.0 30.0 43.0
1.00

14. 
.k = kP
ii
i=1
n

k = expected rate of return.
k
HT = 0.10(-22%) + 0.20(-2%)
+ 0.40(20%) + 0.20(35%)
+ 0.10(50%) = 17.4%.
^
^

15.  HT has the highest rate of return.
 Does that make it best?
k
HT 17.4%
Market 15.0
USR 13.8
T-bill 8.0
Collections 1.7
^

16. No, Check The Risk First

17. Risk
Standard deviation measures the stand-alone risk of an
investment.
The larger the standard deviation, the higher the
probability that returns will be far below the expected
return.
Coefficient of variation is an alternative measure of
stand-alone risk.

18.  .Pk
ˆ
k
Variance
deviation Standard
n
1i
i
2
i
2






19. 
T-bills = 0.0%.

HT = 20.0%.

Coll=13.4%.

USR
=18.8%.

M=15.3%.
 .Pk
ˆ
k
n
1i
i
2
i


HT:
 = ((-22 - 17.4)
2
0.10 + (-2 - 17.4)
2
0.20
+ (20 - 17.4)
2
0.40 + (35 - 17.4)
2
0.20
+ (50 - 17.4)
2
0.10)
1/2
= 20.0%.

20.  Which alternative is best?
Expected
Security return Risk, 
HT 17.4% 20.0%
Market 15.0 15.3
USR 13.8 18.8
T-bills 8.0 0.0
Collections

1.7 13.4

21. The T-bill will return 8% regardless
of the state of the economy.
Is the T-bill riskless? Explain.

22. HT moves with the economy, so it is
positively correlated with the economy.
This is the typical situation.
Collections moves counter to the
economy. Such negative correlation is
unusual.

23. Another way to measure risk of an investment
It’s the relative standard deviation to expected
return
CV = std / ER
Measures risk per unit of return
It is useful for investment with diff expected
returns

24. Standard deviation tells us the fluctuations of
returns
While CV tells us the relative risk againt the
expected return
Like if CV is 5% it means for every 1 unit of
return there is 5% risk