chapter 12 financial return and risk concepts © 2000 john wiley & sons, inc
TRANSCRIPT
![Page 1: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/1.jpg)
Chapter 12
Financial Return and Risk Concepts
© 2000 John Wiley & Sons, Inc.
![Page 2: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/2.jpg)
2
Describe the difference between historical and expected rates of return.
Know how to compute arithmetic averages, variances, and standard deviations using return data for a single financial asset.
Know the historical rates of return and risk for different securities.Explain the three forms of market efficiency.Explain how to calculate the expected return on a portfolio of securities.
Chapter Outcomes
![Page 3: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/3.jpg)
3
Understand how and why the combining of securities into portfolios reduces the overall or portfolio risk.
Explain the difference between systematic and unsystematic risk.
Explain the meaning of “beta” coefficients and describe how they are calculated.
Describe the capital asset pricing model (CAPM) and discuss how it is used.
Chapter Outcomes
![Page 4: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/4.jpg)
4
Historical Return and Risk for a Single Asset
Return: periodic income and price changes
Can be daily, monthly…but we’ll focus on annual returns
Risk: based on deviations over time around the average return
![Page 5: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/5.jpg)
5
Returns for Two Stocks Over Time
![Page 6: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/6.jpg)
6
Arithmetic Average Return
Look backward to see how well we’ve done:
Average Return (AR) =
Sum of returns
number of years
![Page 7: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/7.jpg)
7
An Example
YEAR STOCK A STOCK B
1 6% 20%
2 12 30
3 8 10
4 –2 –10
5 18 50
6 6 20
Sum 48 120
Sum/6 = AR= 8% 20%
![Page 8: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/8.jpg)
8
Measuring Risk
Deviation = Rt - AR
Sum of Deviations (Rt - AR) = 0 To measure risk, we need something
else…try squaring the deviations
Variance 2
= (Rt - AR)2
n - 1
![Page 9: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/9.jpg)
9
Since the returns are squared:(Rt - AR)2
The units are squared, too: Percent squared (%2)
Dollars squared ($ 2)
Hard to interpret!
![Page 10: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/10.jpg)
10
Standard deviation
The standard deviation () helps this problem by taking the square root of the variance:
2=
![Page 11: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/11.jpg)
11
A’s RETURN RETURN
DIFFERENCE FROM DIFFERENCE
YR THE AVERAGE SQUARED
1 6%– 8% = –2% (–2%)2 = 4%2
2 12 – 8 = 4 (4)2 = 16
3 8 – 8 = 0 (0)2 = 0
4 –2 – 8 = –10 (–10)2 = 100
5 18– 8 = 10 (10)2 = 100
6 6 – 8 = –2 (-2)2 = 4
Sum 224%2
Sum/(6 – 1) = Variance 44.8%2
Standard deviation = 44.8 = 6.7%
![Page 12: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/12.jpg)
12
Using Average Return and Standard Deviation
If the periodic return are normally distributed
68% of the returns will fall between AR - and AR +
95% of the returns will fall between AR - 2 and AR + 2
95% of the returns will fall between AR - 3 and AR + 3
![Page 13: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/13.jpg)
13
For Asset A
If the returns are normal, over time we should see:
68% of the returns between 1.3% and 14.7%
95% of the returns between -5.4% and 21.4%
99% of the returns between -12.1% and 28.1%
![Page 14: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/14.jpg)
14
Which of these is riskier?
Asset A Asset B
Avg. Return 8% 20%
Std. Deviation 6.7% 20%
![Page 15: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/15.jpg)
15
Another view of risk:
Coefficient of Variation =
Standard deviation
Average return
It measures risk per unit of return
![Page 16: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/16.jpg)
16
Which is riskier?
Asset A Asset B
Avg. Return 8% 20%
Std. Deviation 6.7% 20%
Coefficient
of Variation 0.84 1.00
![Page 17: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/17.jpg)
17
Measures of Expected Return and Risk
Looking forward to estimate future performance
Using historical data: ex-post Estimated or expected outcome: ex-ante
![Page 18: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/18.jpg)
18
Steps to forecasting Return, Risk Develop possible future scenarios:
– growth, normal, recession Estimate returns in each scenario:
– growth: 20%– normal: 10%– recession: -5%
Estimate the probability or likelihood of each scenario:
growth: 0.30 normal: 0.40 recession: 0.30
![Page 19: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/19.jpg)
19
Expected Return
E(R) = pi . Ri
E(R) =
.3(20%) + .4(10%) +.3(-5%) = 8.5% Interpretation:
8.5% is the long-run average outcome if the current three scenarios could be replicated many, many times
![Page 20: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/20.jpg)
20
Once E(R) is found, we can estimate risk measures:
2 = pi[ Ri - E(R)] 2
= .3(20 - 8.5)2 + .4(10 - 8.5)2
+ .3(-5 - 8.5)2
= 95.25 percent squared
![Page 21: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/21.jpg)
21
Standard deviation:
= 95.25%2 = 9.76%
Coefficient of Variation = 9.76/8.5 = 1.15
![Page 22: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/22.jpg)
22
Historical Returns and Risk of Different Assets
Two good investment rules to remember:
Risk drives returns
Developed capital markets, such as those in the U.S., are, to a large extent, efficient markets.
![Page 23: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/23.jpg)
23
Efficient Markets
What’s an efficient market? Many investors/traders News occurs randomly Prices adjust quickly to news,
reflecting the impact of the news and market expectations
![Page 24: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/24.jpg)
24
More….
After adjusting for risk differences, investors cannot consistently earn above-average returns
Expected events don’t move prices; only unexpected events (“surprises”) move prices
![Page 25: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/25.jpg)
25
Price Reactions in Efficient/Inefficient Markets
Overreaction(top)
Efficient (mid)
Underreaction
(bottom)
Good news event
![Page 26: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/26.jpg)
26
Types of Efficient Markets
Strong-form efficient market Semi-strong form efficient market Weak-form efficient market
![Page 27: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/27.jpg)
27
Implications of “Efficient Markets”
Market price changes show corporate management the reception of announcements by the firm
Investors: consider indexing rather than stock-picking
Invest at your desired level of risk Diversify your investment portfolio
![Page 28: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/28.jpg)
28
Portfolio Returns and Risk
Portfolio: a combination of assets or investments
![Page 29: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/29.jpg)
29
Expected Return on A Portfolio:
E(Ri) = expected return on asset i
wi = weight or proportion of asset i in the portfolio
E(Rp) = wi . E(Ri)
![Page 30: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/30.jpg)
30
If E(RA) = 8% and E(RB) = 20%
More conservative portfolio:
E(Rp) = .75 (8%) + .25 (20%) = 11%
More aggressive portfolio:
E(Rp) = .25 (8%) + .75 (20%) = 17%
![Page 31: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/31.jpg)
31
Possibilities of Portfolio “Magic”
The risk of the portfolio may be less than the risk of its component assets
![Page 32: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/32.jpg)
32
Merging 2 Assets into 1 Portfolio
Two risky assets become a low-risk portfolio
![Page 33: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/33.jpg)
33
The Role of Correlations
Correlation: a measure of how returns of two assets move together over time
Correlation > 0; the returns tend to move in the same direction
Correlation < 0; the returns tend to move in opposite directions
![Page 34: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/34.jpg)
34
Diversification
If correlation between two assets (or between a portfolio and an asset) is low or negative, the resulting portfolio may have lower variance than either asset.
Illustrates diversification benefits.
![Page 35: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/35.jpg)
35
The Two Types of Risk
Diversification shows there are two types of risk:
Risk that can be diversified away (diversifiable or unsystematic risk)
Risk that cannot be diversified away (undiversifiable or systematic or market risk)
![Page 36: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/36.jpg)
36
Capital Asset Pricing Model
Focuses on systematic or market risk
An asset’s risk depend upon whether it makes the portfolio more or less risky
The systematic risk of an asset determines its expected returns
![Page 37: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/37.jpg)
37
The Market Portfolio
Contains all assets--it represents the “market”
The total risk of the market portfolio (its variance) is all systematic risk
Unsystematic risk is diversified away
![Page 38: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/38.jpg)
38
The Market Portfolio and Asset Risk
We can measure an asset’s risk relative to the market portfolio
Measure to see if the asset is more or less risky than the “market”
More risky: asset’s returns are usually higher (lower) than the market’s when the market rises (falls)
Less risky: asset’s returns fluctuate less than the market’s over time
![Page 39: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/39.jpg)
39
Blue = market returns over timeRed = asset returns over time
More systematic risk than market
Less systematic risk than market
Return
Time0%
Asset Market
Time0%
![Page 40: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/40.jpg)
40
Implications of the CAPM
Expected return of an asset depends upon its systematic risk
Systematic risk (beta ) is measured relative to the risk of the market portfolio
![Page 41: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/41.jpg)
41
Beta example: < 1
If an asset’s is 0.5: the asset’s returns are half as variable, on average, as those of the market portfolio
If the market changes in value by 10%, on average this assets changes value by 10% x 0.5 = 5%
![Page 42: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/42.jpg)
42
> 1
If an asset’s is 1.4: the asset’s returns are 40 percent more variable, on average, as those of the market portfolio
If the market changes in value by 10%, on average this assets changes value by 10% x 1.4 = 14%
![Page 43: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/43.jpg)
43
Sample Beta Values
Firm Beta
AT&T 0.75
Coca-Cola 1.10
GE 1.20
AMR 1.30
Amer. Electric
Power 0.55
![Page 44: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/44.jpg)
44
Learning Extension 12AEstimating Beta
Beta is derived from the regression line:
Ri = a + RMKT + e
![Page 45: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/45.jpg)
45
Ways to estimate Beta
Once data on asset and market returns are obtained for the same time period:
use spreadsheet software statistical software financial/statistical calculator do calculations by hand
![Page 46: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/46.jpg)
46
Sample Calculation
Estimate of beta:
n(RMKTRi) - (RMKTRi)
n RMKT2 - (RMKT)2
![Page 47: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/47.jpg)
47
The sample calculationEstimate of beta =
n(RMKTRi) - (RMKT Ri)
n RMKT2 - (RMKT)2
6( 0.2470) - (0.72)(1.20)
6(0.1406) - (0.72)(0.72)
= 1.90
![Page 48: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/48.jpg)
48
Security Market Line
CAPM states the expected return/risk tradeoff for an asset is given by the Security Market Line (SML):
E(Ri)= RFR + [E(RMKT)- RFR]i
![Page 49: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/49.jpg)
49
An Example
E(Ri)= RFR + [E(RMKT)- RFR]i
If T-bill rate = 4%, expected market return = 8%, and beta = 0.75:
E(Rstock)= 4% + (8% - 4%)(0.75) = 7%
![Page 50: Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc](https://reader033.vdocument.in/reader033/viewer/2022061306/551490e7550346d36e8b521c/html5/thumbnails/50.jpg)
50
Portfolio beta
The beta of a portfolio of assets is a weighted average of its component asset’s betas
betaportfolio = wi. betai