Risk and Return
Stand-alone and Portfolio Considerations
Financial Management
Topics Covered
Basic return concepts
Basic risk concepts
Stand-alone risk
Portfolio (market) risk
Risk and return: CAPM/SML
What are investment returns?
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.
Why do we invest?
To make money on our money.
year-to-year returns
Calculate the average annual return
What is investment risk?
Typically, investment returns are not known with certainty.
Investment risk pertains to the probability of earning a return less than that expected.
The greater the chance of a return far below the expected return, the greater the risk.
Continuous Probability Distribution
Rate of
return (%)
50
15
0
-20
Stock X
Stock Y
Calculate the expected rate of return
r = expected rate of return.
^
Standard Deviation
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.
Probability Distribution
Page 111
Rate of
return (%)
60
8
0
Stock X
Stock Y
Which stock is riskier? Why?
Return vs. Risk: Which investment is best?
Investment in Different Types of Portfolios: 1926-1998
Year-to-Year Total Returns on Small Company Common Stocks: 1926-1998
Year-to-Year Total Returns on Large Company Common Stocks: 1926-1998
Year-to-Year Total Returns on Bonds and Bills: 1926-1998
Historical Returns, Standard Deviations, and Frequency Distributions: 1926-1998
Risk and Return
Stand-alone and Portfolio Considerations
Financial Management
Two-Stock Portfolios
Two stocks can be combined to form a riskless portfolio if r = .
Risk is not reduced at all if the two stocks have r = +.
In general, stocks have r , so risk is lowered but not eliminated.
Investors typically hold many stocks.
What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?
p would decrease because the added stocks would not be perfectly correlated, but rp would remain relatively constant.
^
# Stocks in Portfolio
10 20 30 40 2,000+
Company Specific (Diversifiable) Risk
Market Risk
20
0
Stand-Alone Risk, p
p (%)
35
Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.
Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.
Conclusions
As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.
p falls very slowly after about 40 stocks are included. The lower limit for p is about 20% = M .
By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.
Relevant risk, which is relevant for stocks held in well-diversified portfolios, is defined as contribution of a security to the overall riskiness of the portfolio.
It is measured by a stock’s beta coefficient. For stock i, its beta is:
bi = ( si / sM ) * riM
How is relevant risk measured for individual securities?
How is beta interpreted?
If b = , stock has average risk.
If b > , stock is riskier than average.
If b < , stock is less risky than average.
Most stocks have betas in the range of to .
Can a stock have negative beta?
Beta
Beta is another measure of risk.
Based on the concept that market risk or overall volatility of the market is not something an investor can control.
Beta measures movement of the stock in relation to market.
Using a Regression to Estimate Beta
Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.
The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.
Calculating Beta in Practice
Many analysts use the S&P 500 to find the market return.
Analysts typically use four or five years’ of monthly returns to establish the regression line.
Some analysts use 52 weeks of weekly returns.
Use the historical stock returns to calculate the beta for KWE.
%
%
10
%
%
9
%
%
8
%
%
7
%
%
6
%
%
5
%
%
4
%
%
3
%
%
2
%
%
1
KWE
Market
Year
Calculating Beta for KWE
r
KWE
=
M
+
R
2
=
-40%
-20%
0%
20%
40%
-40%
-20%
0%
20%
40%
r
M
r
KWE
相关系数对样本相关关系的计量
不同产业的贝塔值变动状况表
陈伟忠《动态组合理论与中国证券资产定价》
1990年12月19日至1997年月间
综合类
公用事业类
房地产类
商业类
工业类
变异系数
标准差
贝塔均值
产业
福建
广东
东北
山东
华中
上海
华北
北京
陕西
浦东
四川
江浙
变异系数
标准差
贝塔均值
地域
Use the SML to calculate each
alternative’s required return.
The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM).
SML: ri = rRF + (RPM)bi .
Assume rRF = 8%; rM = 15%.
RPM = (rM - rRF) = 15% - 8% = 7%.
.
rM = 15
rRF = 8
-1 0 1 2
.
SML: ri = rRF + (RPM) bi
ri = 8% + (7%) bi
ri (%)
Risk, bi
SML and Investment Alternatives
Market
SML1
Original situation
Required Rate
of Return r (%)
SML2
0
18
15
11
8
New SML
I = 3%
Impact of Inflation Change on SML
Risk, bi
rM = 18%
rM = 15%
SML1
Original situation
Required Rate of Return (%)
SML2
After increase
in risk aversion
Risk, bi
18
15
8
RPM = 3%
Impact of Risk Aversion Change on SML
2
There are two ways to make money on our money or get a return on your money: capital gains and income.
We break it down for at least two good reasons.
Some investments may give either one or another of these and you evaluate each differently.
Uncle Sam makes a distinction between these two types of returns.
What we’ve done here is combine the gain and dividend yield for each stock. Let’s take 1998 for McDonald’s. At the beginning of the year, McDonald’s sold for $. At the end of the year, it sold for $. That’s a gain of $. In 1998, McDonald’s gave cents in dividends. The total amount you made on McDonald’s for the year would be the combination of both gain and yield or $. Take that and divide by the price at the beginning of the years and you get % return for the year. We did this same calculation for all the other years. Then we did the same calculation for 3M.
It would be as if you bought the stock at the end of one year and sold at the end of the next. This gives the annual return for each stock.
Now this just verifies what we saw in the graph. Some years McDonald’s did better and some years 3M did better.
Here’s McDonald’s and 3M. Again companies you’re pretty familiar with. (3M makes Post-it notes and a lot of other things).
Now let’s say you’re trying to decide between McDonald’s and 3M as an investment. Which would you choose. If you look year to year, it’s tough to figure out. Some years McDonalds is the best while other years 3M wins out.
In order to smooth out the ups and downs, we calculate the average.
How do we calculate average? What if we wanted the average age of this class. (Ask for learner response.)
One of the ways investors try to predict how a stock will perform in the future is by taking the average. Averages are used all the time to describe things and predict what might happen. For example, if you want to know what the weather in a place might be, you’ll look at the average temperature for the season. Averages are calculated by taking all the values and dividing by the number. For example, take the day-time temperature every day in summer and divide by the number of days in summer.
To calculate the average annual stock return, you take the return every year and divide by the number of years. We’re used 5 years in this case. McDonald’s annual returns are 1%, 6%, 62%, 5% and -15%. Add all those up and divide by 5, you get 12%. You do the same for 3M and you get 20%. Which do you buy?
If you look at the averages, 3M has a better average return. (It’s not quite that simple but it’s a starting point.)
If we could just use averages to predict the future, investing would be simple but investments don’t follow any fixed trend. Another measure investors look at is how much the returns move up and down.
In this case we’re looking at the simplest measure of up-and-downess and that’s range. McDonalds maximum or largest annual return is 62%. It’s minimum or smallest annual return is -15%. The difference between the two of these is the range or 77%. (Be careful when you subtract a negative number it becomes positive.) 3M’s range is 52%. As an investor, you know that McDonald’s returns move more up and down than 3M.
Hold this thought for when we cover risk later in this module.
2
3
8
10
13
3
When financial pros assess investments, they like to plot them on graphs where the axes are increasing return (y-axis or vertical axis) and increasing risk (x-axis or horizontal axis). As an investor, where would you like your stocks to be on this chart? The most desirable place (see below) is the Northwest (of course!) quadrant. This quadrant has the highest return and the least risk. (Most investment advisors claim they can take you there.)
But wait a minute. Does this mean that if you take more risk you’re going to get a better return? NO! Not all investments follow the rules. Look at Japanese stocks in the 90s. They had tremendous volatility and no return!
22
25
27
29
31
34
39
Now we spent a lot of time talking about the economy, inflation, interest rates and investment returns in the last module. One main point we made was the that market is going to rise and fall and there ain’t a thing we can do about that. (It’s what finance types call systemic risk.) We know to leave moderating market risk to the Federal Reserve or other very large and influential bodies.
When we look at a measure like standard deviation, it’ll include market up and downs in the variability it measures. Some finance types want to separate this market risk from the risk of the investment itself. So they came up with the measure called beta. It tells you how your investment is moving against some standard or index.
Now we can get into the math of beta later but you can use some rule of thumbs when looking at beta. A beta of one means the investment moves just like the market. A beta of more than one means the investment is more volatile than the market. A beta of less than one means it is less volatile than the market.
Usually you can figure this out intuitively. Think about Yahoo, would it have a beta of more or less than one? Think about Anheuser Busch (BUD beer), would it have a beta of more or less than one?
35
37
35
43
46
50
52
