an introduction to risk and retur
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An Introduction to Risk and ReturTRANSCRIPT
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Chapter 4
An Introduction to Risk and Return
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Slide Contents
Learning Objectives
1. Calculate Realized and Expected Rates of Return.
2. Compute Geometric and Arithmetic Average Rates of Return.
3. Defining Risk and Calculating risk
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Principles Used in This Chapter
Principle 1: There is a Risk-Return Tradeoff.
We will expect to receive higher returns for assuming more risk.
Principle 2: Market Prices Reflect Information.
Depending on the degree of efficiency of the market, security prices
may or may not fully reflect all information.
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Investment Process
1. Market and Security Analysis
2. Formation of Optimal Portfolio
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Return
Income received on an investment plus any change
in market price, usually expressed as a percent
of the beginning market price of the investment.
The total gain or loss experienced on an investment over a
given period of time.
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Calculating the Realized Return from an
Investment
Realized return or cash return measures the gain or loss on an
investment.
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Calculating the Realized Return from an
Investment (cont.)
We can also calculate the rate of return as a percentage. It is
simply the cash return divided by the beginning stock price.
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Calculating the Realized Return from an
Investment (cont.)
Example 1: You invested in 1 share of Apple (AAPL) for $95 and
sold a year later for $200. The company did not pay any dividend
during that period. What will be the cash return on this
investment?
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Calculating the Realized Return from an
Investment (cont.)
Cash Return = $200 + 0 - $95
= $105
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Calculating the Realized Return from an
Investment (cont.)
Example 2: You invested in 1 share of share Apple (AAPL) for $95
and sold a year later for $200. The company did not pay any
dividend during that period. What will be the rate of return on
this investment?
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Calculating the Realized Return from an
Investment (cont.)
Rate of Return = ($200 + 0 - $95) ÷ 95
= 110.53%
Table 7-1 has additional examples on measuring an investor’s realized rate
of return from investing in common stock.
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Calculating the Realized Return from an
Investment (cont.)
Table 7-1 indicates that the returns from investing in common
stocks can be positive or negative.
Furthermore, past performance is not an indicator of future
performance.
However, in general, we expect to receive higher returns for
assuming more risk.
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Calculating the Expected Return from an
Investment
Expected return is what you expect to earn from an
investment in the future.
It is estimated as the average of the possible returns, where each
possible return is weighted by the probability that it occurs.
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Calculating the Expected Return from an
Investment (cont.)
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Calculating the Expected Return from an
Investment (cont.)
Expected Return
= (-10%×0.2) + (12%×0.3) + (22%×0.5)
= 12.6%
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Measuring Risk
In the example on Table 7-2, the expected return is 12.6%;
however, the return could range from -10% to +22%.
This variability in returns can be quantified by computing the
Variance or Standard Deviation in investment returns.
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Geometric
vs. Arithmetic Average
Rates
of Return
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Geometric vs. Arithmetic Average Rates of
Return
Arithmetic average may not always capture the true rate of return
realized on an investment.
In some cases, geometric or compound average may be a more
appropriate measure of return.
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Geometric vs. Arithmetic Average Rates of
Return (cont.)
For example, suppose you bought a stock for $25. After one year,
the stock rises to $30 and in the second year, it falls to $15. What
was the average return on this investment?
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Geometric vs. Arithmetic Average Rates of
Return (cont.)
The stock earned +20% in the first year and -50% in the second
year.
Simple average = (20%-50%) ÷ 2 = -15%
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Computing Geometric Average Rate of
Return
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Geometric vs. Arithmetic Average Rates of
Return (cont.)
However, over the 2 years, the $25 stock lost the equivalent of
22.54%
{(1+.20)(1-.50)}1/2 - 1 = -22.54%.
Here, -15% is the simple arithmetic average while -22.54% is the
geometric or compound average rate.
Which one is the correct indicator of return? It depends on the
question being asked.
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Geometric vs. Arithmetic Average Rates of
Return (cont.)
The geometric average rate of return answers the question,
“What was the growth rate of your investment?”
The arithmetic average rate of return answers the question, “what
was the average of the yearly rates of return?
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Computing Geometric Average Rate of
Return (cont.)
Compute the arithmetic and geometric average for the following
stock.
Year Annual Rate of Return
Value of the stock
0 $25
1 40% $35
2 -50% $17.50
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Computing Geometric Average Rate of
Return (cont.)
Arithmetic Average = (40-50) ÷ 2 = -5%
Geometric Average
= [(1+Ryear1) × (1+Ryear 2)]1/2 - 1
= [(1.4) × (.5)] 1/2 - 1
= -16.33%
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Choosing the Right “Average”
Both arithmetic average geometric average are important and correct. The following
grid provides some guidance as to which average is appropriate and when:
Question being addressed:
Appropriate Average Calculation:
What annual rate of return can we expect for next year?
The arithmetic average calculated using annual rates of return.
What annual rate of return can we expect over a multi-year horizon?
The geometric average calculated over a similar past period.
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Checkpoint 7.2
Computing the Arithmetic and Geometric Average Rates of Return
Five years ago Mary’s grandmother gave her $10,000 worth of stock in the shares of a publicly traded company
founded by Mary’s grandfather. Mary is now considering whether she should continue to hold the shares, or
perhaps sell some of them. Her first step in analyzing the investment is to evaluate the rate of return she has
earned over the past five years.
The following table contains the beginning value of Mary’s stock five years ago as well as the values at the end of
each year up until today (the end of year 5):
What rate of return did Mary earn on her investment in the stock given to her by her grandmother?
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Checkpoint 7.2
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Checkpoint 7.2: Check Yourself
• Mary has decided to keep the stock given to her by her grandmother. However, now she wants to consider the prospect of selling another gift made to her five years ago by her grandmother. What are the arithmetic and geometric average rates of return for the following investment?
• See table on the next slide.
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Problem (cont.)
Year Annual Rate of Return
Value of the Stock
0 $10,000.00
1 -15.0% $8,500.00
2 15.0% $9,775.00
3 25.0% $12,218.75
4 30.0% $15,884.38
5 -10.0% $14,295.94
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Step 2: Decide on a Solution Strategy
We need to calculate the arithmetic and geometric average.
The arithmetic average fails to capture the effect of compound
interest, which can be measured by geometric average.
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Step 3: Solve
Calculate the Arithmetic Average
Arithmetic Average
= Sum of the annual rates of return ÷ Number of years
= 45% ÷ 5 = 9%
Based on past performance of the stock, Mary should expect that
it would earn 9% next year.
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Step 3: Solve (cont.)
Calculate the Geometric Average
Geometric Average = [(1+Ryear1) × (1+Ryear 2 ) × (1+Ryear3) × (1+Ryear4)
× (1+Ryear5) ]1/5 - 1
= [(.85) × (1.15) × (1.25) × (1.30) × (.90)] 1/5 - 1
= 7.41%
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Step 4: Analyze
The arithmetic average is 9% while the geometric average is
7.41%. The geometric average is lower as it incorporates
compounding of interest.
Both of these averages are useful and meaningful but in answering
two very different questions.
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Step 4: Analyze (cont.)
The arithmetic average answers the question, what rate of return
Mary can expect from her investment next year assuming all else
remains the same as in the past?
The geometric average answers the question, what rate of return
Mary can expect over a five-year period?
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Defining Risk
The variability of returns from those that are expected.
The chance of financial loss or more formally the variability
of returns associated with a given asset.
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Market Risk
The chance that the value of an investment will affect because
of market factors such as economic, political &social events.
In general, the more a given investment’s value responds to
the market, the greater its risk & vice versa.
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Interest rate risk
The chance that the changes in interest rates will adversely
affect the value of an investment.
Most investments lose value when the interest rate rises &
increases in value when it falls
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Inflation Risk
Refers to uncertainty of purchasing power of cash flows to be
received out of investment.
Investment involves a postponement of current
consumption. If during this period prices of goods and
services go up, Investor loses in terms of purchasing power.
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Business Risk
Variability in the income of the firm and the expected
dividend.
Some Industries have higher business risk than others.
Security of firm with higher business risk are risky.
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Financial Risk
Degree of debt financing used by the firm in the capital
structure.
Higher the debt financing, the greater the degree of financial
risk.
Debt Financing increases the risk of equity shares by
- Increasing the variability of returns of equity shares
- -increasing the risk of non-receipt of capital in case of
winding up of company.
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Types of Risk
Out of the five sources of risk in the investments, the first
three are external to the firm and are uncontrollable
Last two risks i.e business risk and the financial risk are
internal to the firm and are controllable.
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Systematic risk
Variability in return due to general factors in the market such
as money supply, inflation, economic recession , interest rate
policy of the government, political factors, credit policy, tax
reforms.
No investor can avoid this risk whatever precaution or
diversification may be resorted to.
It is also called as non-diversifiable risk
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Unsystematic Risk
Fluctuations in return from an investment due to factors that
are specific to the particular firm not the market as a whole.
These are unique to the firm, these must be examined
separately for each firm and the industry
For example, the risk that airline industry employees will go
on strike, and airline stock prices will suffer as a result, is
considered to be unsystematic risk
It is also called as diversifiable risk.
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Measuring Risk
.
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5 10 15
Number of Securities
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Market risk
Unique
risk
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Risk Illustrated
Possible Returns on the Stock
Probability
-30% -20% -10% 0% 10% 20% 30% 40%
Outcomes that produce harm
The range of total possible returns on the stock runs from -30% to more than +40%. If the required return on the stock is 10%, then those outcomes less than 10% represent risk to the investor.
A
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CHAPTER 8 – Risk, Return and Portfolio Theory
8 - 49
Range
The difference between the maximum and minimum values is
called the range.
As a rough measure of risk, range tells us that common stock is
more risky than treasury bills.
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Differences in Levels of Risk Illustrated
Possible Returns on the Stock
Probability
-30% -20% -10% 0% 10% 20% 30% 40%
Outcomes that produce harm The wider the range of probable outcomes the greater the risk of the investment.
A is a much riskier investment than B B
A
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Measuring Risk
Variance - Average value of squared deviations from mean.
A measure of volatility.
Standard Deviation - Average value of squared
deviations from mean. A measure of volatility.
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Measuring Risk
Problem 1
Estimate the standard deviation of the historical returns on
investment A that were:
Time Return
1 10%
2 24%
3 -12%
4 8%
5 10%
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Measuring Risk
Step 1 – Calculate the Historical Average Return
Step 2 – Calculate the Standard Deviation
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Measures of Risk
54
Given an asset's expected return, its variance can be calculated
using the following equation:
N
Var(r) = 2 = S pi(ri – E[r])2
i=1
Where:
N = the number of states
pi = the probability of state i
ri = the return on the stock in state i
E[r] = the expected return on the stock
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Measures of Risk
55
The standard deviation is calculated as the positive square root of
the variance:
SD(R) = = 2 = (2)1/2 = (2)0.5
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Measures of Risk
56
Probability Distribution:
State Probability Return On Return On
Stock A Stock B
1 20% 5% 50%
2 30% 10% 30%
3 30% 15% 10%
4 20% 20% -10%
E[r]A = 12.5%
E[r]B = 20%
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Expected Return
57
In this example, the expected return for stock A would be
calculated as follows:
E[r]A = .2(5%) + .3(10%) + .3(15%) + .2(20%) = 12.5%
Now you try calculating the expected return for stock B!
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Expected Return
58
Did you get 20%? If so, you are correct.
If not, here is how to get the correct answer:
E[r]B = .2(50%) + .3(30%) + .3(10%) + .2(-10%) = 20%
So we see that Stock B offers a higher expected return than Stock A.
However, that is only part of the story; we haven't considered risk.
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Measures of Risk
59
The variance and standard deviation for stock A is calculated as follows:
2A = .2(.05 -.125)2 + .3(.1 -.125)2 + .3(.15 -.125)2 + .2(.2 -.125)2 = .002625
A (.002625)0.5 .0512 5.12%
Now you try the variance and standard deviation for stock B!
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Measures of Risk
60
If you didn’t get the correct answer, here is how to get it:
2
B = .2(.50 -.20)2 + .3(.30 -.20)2 + .3(.10 -.20)2 + .2(-.10 - .20)2 = .042
B (.042)0.5 .2049 20.49%
Although Stock B offers a higher expected return than Stock A, it also is riskier since its variance and standard deviation are greater than Stock A's.
This, however, is still only part of the picture because most investors choose to hold securities as part of a diversified portfolio.