Title: Introduction to Finance: Risk and Return
1Introduction to FinanceRisk and Return
2Invest?
- Investment A yields a return of about 12 per
year on average (?????12). - Investment B yields a return of about 8 per
year on average. - Investment C yields a return of about 5 per
year on average. - Which investment would you choose? Why?
3Defining Return
- For example, purchase Take-chan stock yesterday
at 1000 yen per share. - Today, you sell the shares at the market price
1100 yen. In other words, the stock priced
increased by 100 yen over one day. - What is your percentage gain?
- (1100-1000)/1000 100/10000.1
- Return is 10 (one day).
4Return (???)(Pt-Pt-1)/Pt-1
Pt-1
Pt
Yesterday (t-1)
Today (t)
Pstock price (??)
5Risk?
- What is risk?
- Much of finance is about risk.
- Buying and selling risk in the market.
- What is the correct price for holding (buying or
selling) risk? - How much risk should be bought or sold?
6Measuring Risk
- Be able to distinguish between risk which is
rewarded and not rewarded. - Measure should be applicable to as many assets as
possible. Standardized to facilitate comparison
across assets. - Need a measure of risk which can be compared
across assets/projects. Thus a standardized
measure.
7Cont.
- Need a measure which can be translated into
expected return (opportunity cost of
capital/equity). - required return riskfree rate premium
8Relative Dispersion of Returns
- One measure of risk is the relative dispersion of
returns. - How many returns are above average?
- How many returns are below average?
- Notice we are creating a measure relative to the
average.
9Calculate Historical Annual Returns (?????)
return
return
P94
P95
P96
P97
P98
P99
P00
P01
01
00
98
97
96
95
94
99
10Plot Historical Returns (Histogram)
Number of Observations (return)
4
Return
0
Positive returns
Negative returns
11One way of characterizing the distribution of
returns in the future.
Small probability of very low (very
negative) returns (Recession).
Low probability of very high returns (Boom).
12Distribution (??)
Frequency
Dispersion, Variability is depicted by the
spread in the distribution.
Return
Expected Return (?????)
13Variance (??)
- One statistical measure (???) of this spread is
variance (??). - This measures variability relative to the mean or
average (???). - The square root of the variance is called the
standard deviation (????).
14Variance (??)
Frequency
Take Difference And Square
Return
expected Return (?????)
Ret1
15Sample Variance (Historical Data)
- Take the difference between the observed return
and the average return. - Square each of the above differences.
- Square each difference to avoid positive and
negative differences from canceling. - Add all the squared differences.
16Cont.
- Take the average of the squared differences. In
other words, divide the sum of the squared
differences by the number of observations less
one (degrees of freedom,???). - Thus, the variance is an average as well.
17Year 01 00 99 98 97 96 95 Return 10 -5 5 -6
-10 0 6
Average or Mean Return0
Variance ? Standard Deviation ?
18- A larger variance (standard deviation) means
there is a greater spread or variability. - Thus a larger variance would mean greater risk.
- A smaller variance would mean relatively less
risk.
19Same Average (expected) Return but
Different Variances
Return
(?????)
Return
(?????)
20Which would you choose?
- Stock with standard deviation of 15 (average
return 5) - Stock with standard deviation of 20 (average
return 5)
21Our original question?
- Investment A yields a return of about 12 per
year on average. Standard Deviation 18. - Investment B yields a return of about 8 per
year on average. Standard Deviation 6. - Investment C yields a return of about 5 per
year on average. Standard Deviation 1. - P. 91 text
22Measuring Risk as Standard Deviation
23Examples Risk-Return
- P. 92 Text (Look at Graph)
- P. 102 Text (Table 5-3)
- We can plot each security (stock) in risk-return
space.
24Plotting Risky Assets
Expected Return (?????)
stock 1
ret 1
ret 2
Risk( ???) standard deviation (????)
stock 2
std dev 2
std dev 1
25Expected Return
Risk standard deviation