return, risk, and the sml
DESCRIPTION
Return, Risk, and the SML. RWJ-Chapter 13. Dividends. Ending market value. Time. 0. 1. Initial investment. Returns. Dollar Returns the sum of the cash received and the change in value of the asset, in dollars. Percentage Returns - PowerPoint PPT PresentationTRANSCRIPT
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Return, Risk, and the SMLRWJ-Chapter 13
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+Returns Dollar Returns
the sum of the cash received and the change in value of the asset, in dollars.
Time 0 1
Initial investment
Ending market value
Dividends
β’ Percentage Returnsβ the sum of the cash received
and the change in value of the asset divided by the original investment.
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+Holding Period Return (Simple Return)
π»ππ =πΈπππππ πππππππ π hπ πππβπ΅ππππππππ πππππ+ hπΆππ π·ππ£πππππ
π΅πππππππππππππ
OR
π»ππ =πΈπππππ πππππππ π hπ πππβπ΅ππππππππ πππππ
π΅ππππππππ πππππ +hπΆππ π·ππ£πππππ
π΅πππππππππππππ
Capital Gain Dividend Yield
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+HPR (Simple Return)-Example (1) Suppose you bought 100 shares of Wal-Mart (WMT) one
year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share Γ 100 shares). At the end of the year, the stock sells for $30. How did you do?
What is your return on this investment?
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+Dollar Return:
$520 gain
Time 0 1
-$2,500
$3,000
$20
Percentage Return:
20.8% = $2,500$520
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+HPR (Simple Period)- Example (2) Letβs look at Ford
π»ππ π½π’ππ¦β π΄π’ππ’π π‘=9.44β9.24+0.05
9.24 =9.44β9.19
9.19 =2.7 %
π»ππ π½π’ππ¦β π΄π’ππ’π π‘=9.44β9.24
9.24 +0.059.24
Dividend Yield=0.54%
Capital Gain=2.16%%Source=Yahoo Finance
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+HPR- Multiple Periods
The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri:
Compounding Return: The cumulative effect that a series of gains or losses on an original amount of capital over a period of time
1)1()1()1( 21 nrrrHPR
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+HPR (Multiple Periods)- Example (3)
Suppose your investment provides the following returns over a four-year period:
Year Return1 10%2 -5%3 20%4 15% %21.444421.
1)15.1()20.1()95(.)10.1(1)1()1()1()1(
return period holdingYour
4321
rrrr
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+HPR (Multiple Periods)- Example (4) Letβs find compounded return for Ford
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+Annualizing Return
How can I annualize my return over time? Two ways:
Arithmetic Average Geometric Average
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+Example
Average (Arithmetic Return)? Geometric Return? Interpret the results
Year Return1 10%2 -5%3 20%4 15%
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+Risk:
What is risk? Websterβs dictionary: βexposing to loss or damageβ In finance:
Stand-alone basis Portfolio basis
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+Which one is more risky? Why?
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+Risk and Return Relation: Is risk a bad?
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+How to measure Risk?
Likelihood that investors will receive a return on an investment that is different from the return they expected to make
Two important key words in this definition Expectations Deviation from our expectations
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+To measure Risk: We need to know two concepts? TIME SERIES ARE GIVEN Expected Return:
How much βactual returnβ deviates from βExpected Returnβ?
πΈ (π )=βπ‘π π‘π
Expected Return
π 2=1π β1βπ‘ (π π‘βπΈ (π ))2
Variance
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+To measure Risk: We need to know two concepts? PROBABILITY DISTRIBUTION GIVEN Probability:
The chance that event will occur
Probability Distribution: If all possible events, or outcomes, are listed, and if
probability is assigned to each event, the listing is called probability distribution.
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+Then:
Expected Return:
How much βactual returnβ deviates from βExpected Returnβ?
πΈ (π )=βπ π (π )Γπ (π )
π 2=βπ π (π )[π (π )βπΈ (π )]2
Expected Return
Variance
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+Example (5)
What is the expected return of Stock X?
πΈ (π π₯ )=(15 %+0 %+5 %+20 %)
4=10 %
π 2=(15 %β10 %)2+(0β10 % )2+(5 %β10% )2+(20 %β10 % )2
4β1=83.33
π=9.12 %
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d1
d2
d3
d4
Standard Deviationβ π12+π22+π32+π42
3
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+Example (6)
What are the expected return for Stocks X and Y?
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+Example (6)-contβd
You have $10,000, what is your portfolio return if you invest $2000 in Stock X and $8000 in Stock Y
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+Diversification and Systematic Risk What is diversification?
Spreading a portfolio over many investments to avoid excessive exposure to any source of risk
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+Diversifiable vs. Market Risk
To the extent that the firm specific influences on two stocks differ, diversification should reduce portfolio risk With all risk sources independent, the exposure to any
particular source of risk is reduced to a negligible level Firm specific risk is called unsystematic, unique risk,
idiosyncratic risk, or diversifiable risk
The risk remains even after extensive diversification. This risk is called market or systematic risk
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+Factors Affecting Unsystematic and Systematic Risk
Unsystematic (Unique) Risk: Successful or unsuccessful product or marketing program Winning or loosing of a major contract In particular: good or bad news for a firm
Systematic Risk: Economic conditions; recession, boom, high inflation, high
interest rates
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+Diversification
Unique Risk
Systematic Risk
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+Market Risk
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+Summary:
Based on the studies on capital market history, we know that there is reward, on average, for bearing risk.
Since, unsystematic risk can be eliminated at virtually no cost (by diversifying), there is no reward for bearing it. Put another way, the market does not reward risks that are borne unnecessarily.
Implication: The expected return on an asset depends only on
that assetβs systematic risk No matter how much total risk an asset has, only the
systematic portion is relevant in determining the expected return
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+How to measure systematic risk? Because systematic risk is the crucial determinant of
an assetβs expected return, we need some way of measuring the level of systematic risk for different investment.
Ξ² (Beta Coefficient) tells us how much systematic risk as an average asset Market Beta=1 Risk Free Rate Beta=0 Stock A: Standard Deviation=40%, Beta=0.50 Stock B: Standard Deviation=20%, Beta=1.50 Ford:
http://www.google.com/finance?q=ford&ei=pISCUtCmIoG20AH2PA
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+Portfolio Beta and Security Market Line Weighted average Betas of the stocks in the portfolio
SML: Expected Return and Systematic Risk Relation:
π½π=βππ€ πΓ π½π
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+Example (7)
Letβs assume that you have a market portfolio (S&P 500) and risk-free rate asset (T-bills). Expected rate of Market Portfolio is 10% and risk-free rate is 3% What is the expected return and Beta if you invest: 100% in risk free rate 75% in risk free rate and 25% in Market Portfolio 50% in risk free rate and 50% in Market Portfolio 25% in risk free rate and 75% in Market Portfolio 100% in Market Portfolio
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+
π ππ€πππ π‘ππ ππ ππ ππ‘ππ=πΈ (π )βπ ππ½
πΆπ΄ππ :πΈ (π π)=π π+π½Γ [πΈ (π π )βπ π ]
Market Risk Premium
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+The SML and the Cost of Capital: A Preview Risk is an extremely important consideration in almost
all business decisions. Therefore, we need to the find the relation between risk and return (the SML)
We also need to know what determines the appropriate discount rate for future cash flows: Market risk premium, risk free rate and Beta
Why is the SML important: It tells us reward to risk in financial markets In order to find the discount rate: we need to compare the
expected return on that investment to what the financial market offers on an investment with the same beta. In other words, the SML line tells us the βgoing rateβ for bearing risk in the economy.
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+The SML and the Cost of Capital: A Preview Cost of Capital: the appropriate discount rate on a new
project is the minimum expected rate of return an investment must offer to be attractive
This minimum required rate of return is called βCost of Capitalβ
We have a much better idea of what determines the required return on invesment.