risk and rates of return
DESCRIPTION
Risk and Rates of Return. Chapter 6. Interest Rate. Interest rate represents the cost of money It is the opportunity cost of money: It shows the return lost from not investing in a comparable risk investment. It is expected to compensate the investor for the time, inflation, and risk. - PowerPoint PPT PresentationTRANSCRIPT
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1
Risk and Rates of Risk and Rates of ReturnReturn
Chapter 6Chapter 6
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4Interest RateInterest Rate
Interest rate represents the cost of moneyInterest rate represents the cost of moneyIt is the opportunity cost of money:It is the opportunity cost of money:
It shows the return lost from not investing in a comparable risk investment.
It is expected to compensate the investor for the time, inflation, and risk.
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5Interest Rates
Conceptually:
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6Interest Rates
Conceptually:
Nominalrisk-freeInterest
Rate
krf
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7Interest Rates
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
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8Interest Rates
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
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9Interest Rates
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
+
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10Interest Rates
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
+
Inflation-risk
premium
IRP
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11
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
+
Inflation-risk
premium
IRP
Mathematically:
Interest Rates
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12
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
+
Inflation-risk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
Interest Rates
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13
Conceptually:
Nominalrisk-freeInterest
Rate
krf
=
Realrisk-freeInterest
Rate
k*
+
Inflation-risk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
This is known as the “Fisher Effect”
Interest Rates
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14
Suppose the real rate is 3%, and the nominal Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium?rate is 8%. What is the inflation rate premium?
(1 + k(1 + krfrf) = (1 + k*) (1 + IRP)) = (1 + k*) (1 + IRP)(1.08) = (1.03) (1 + IRP)(1.08) = (1.03) (1 + IRP)(1 + IRP) = (1.0485),(1 + IRP) = (1.0485), so so
IRP = 4.85%IRP = 4.85%
Interest Rates
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15Term Structure of Interest Rates
The pattern of rates of return for debt The pattern of rates of return for debt securities that differ only in the length securities that differ only in the length of time to maturity.of time to maturity.
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16Term Structure of Interest Rates
The pattern of rates of return for debt The pattern of rates of return for debt securities that differ only in the length securities that differ only in the length of time to maturity.of time to maturity.
yieldto
maturity
time to maturity (years)
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17Term Structure of Interest Rates
The pattern of rates of return for debt The pattern of rates of return for debt securities that differ only in the length securities that differ only in the length of time to maturity.of time to maturity.
yieldto
maturity
time to maturity (years)
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18Term Structure of Interest Rates
yieldto
maturity
time to maturity (years)
The yield curve may be downward sloping or The yield curve may be downward sloping or “inverted” if rates are expected to fall.“inverted” if rates are expected to fall.
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19Term Structure of Interest Rates
yieldto
maturity
time to maturity (years)
The yield curve may be downward sloping or The yield curve may be downward sloping or “inverted” if rates are expected to fall.“inverted” if rates are expected to fall.
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20For a Treasury security, what is the required rate of return?
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21For a Treasury security, what is the required rate of return?
RequiredRequired
rate of rate of
returnreturn==
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22For a Treasury security, what is the required rate of return?
Since Treasuries are essentially Since Treasuries are essentially free of default free of default riskrisk, the rate of return on a Treasury security , the rate of return on a Treasury security is considered the is considered the ““risk-freerisk-free”” rate of return. rate of return.
RequiredRequired
rate of rate of
returnreturn==
Risk-freeRisk-free
rate of rate of
returnreturn
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23
For a corporate stock or bond, what is the required rate of return?
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24
For a corporate stock or bond, what is the required rate of return?
RequiredRequired
rate of rate of
returnreturn==
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25
For a corporate stock or bond, what is the required rate of return?
RequiredRequired
rate of rate of
returnreturn==
Risk-freeRisk-free
rate of rate of
returnreturn
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26
For a corporate stock or bond, what is the required rate of return?
How large of a How large of a risk premiumrisk premium should we require should we require to buy a corporate security? to buy a corporate security?
RequiredRequired
rate of rate of
returnreturn== + +
Risk-freeRisk-free
rate of rate of
returnreturn
RiskRisk
premiumpremium
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27Returns
Expected ReturnExpected Return - the return that an - the return that an investor expects to earn on an asset, investor expects to earn on an asset, given its price, growth potential, etc.given its price, growth potential, etc.
Required ReturnRequired Return - the return that an - the return that an investor requires on an asset given investor requires on an asset given itsits riskrisk and market interest rates.and market interest rates.
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28Risk and Rates of ReturnRisk and Rates of Return
Two Components of returnTwo Components of returnPeriodic cash flowsPeriodic cash flows
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29Risk and Rates of ReturnRisk and Rates of Return
Two Components of returnTwo Components of returnPeriodic cash flowsPeriodic cash flowsPrice Change (capital gains)Price Change (capital gains)
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30Risk and Rates of ReturnRisk and Rates of Return
Holding Period return Holding Period return
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31Risk and Rates of ReturnRisk and Rates of Return
Holding Period return Holding Period return
PPtt + D + Dtt
= ---------- - 1= ---------- - 1 PPt-1t-1
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32Risk and Rates of ReturnRisk and Rates of Return
Holding Period return Holding Period return
PPtt + D + Dtt
= ---------- - 1= ---------- - 1 PPt-1t-1
(P(Ptt - P - Pt-1t-1) + D) + Dtt
= ---------------- = ---------------- PPt-1t-1
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33Risk and Rates of ReturnRisk and Rates of Return
Expected ReturnExpected ReturnExpected return is based on expected cash flows (not
accounting profits)
Return can be expressed as Cash Flows or Percentage Return
Return can be expressed as Cash Flows or Percentage Return
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34Risk and Rates of ReturnRisk and Rates of Return
Expected ReturnExpected ReturnExpected return is based on expected cash flows (not
accounting profits)In an uncertain world future cash flows are not known
with certainty
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35Risk and Rates of ReturnRisk and Rates of Return
Expected ReturnExpected ReturnExpected return is based on expected cash flows (not
accounting profits)In uncertain world future cash flows are not known with
certaintyTo calculate expected return, compute the weighted
average of all possible returns
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36Risk and Rates of ReturnRisk and Rates of Return
Expected ReturnExpected ReturnExpected return is based on expected cash flows (not
accounting profits)In uncertain world future cash flows are not known with
certaintyTo calculate expected return, compute the weighted
average of possible returnsCalculating Expected Return:
k k P ki ii
N
( )
1
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37Risk and Rates of ReturnRisk and Rates of Return
Expected ReturnExpected ReturnExpected return is based on expected cash flows (not
accounting profits)In uncertain world future cash flows are not known with
certaintyTo calculate expected return, compute the weighted
average of possible returnsCalculating Expected Return:
k k P ki ii
N
( )
1
whereki = Return state iP(ki) = Probability of ki occurringN = Number of possible states
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38Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
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39Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
= –0.5%x
k k Pi ii
N
(k )
1
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40Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
= –0.5%= 1%
xx
k k Pi ii
N
(k )
1
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41Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
= –0.5%= 1%= 4%
xxx
k k Pi ii
N
(k )
1
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42Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
= –0.5%= 1%= 4%= 6%
xxxx
k k Pi ii
N
(k )
1
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43Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
= –0.5%= 1%= 4%= 6%
k = 10.5%
xxxx
k k Pi ii
N
(k )
1
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44Risk and Rates of ReturnRisk and Rates of Return
Expected Return CalculationExpected Return Calculation
ExampleExampleYou are evaluating ElCat Corporation’s common stock. You estimate the following returns given different states of the economy
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
= –0.5%= 1%= 4%= 6%
k = 10.5%
Expected (or average) rate of return on stock is 10.5%
Expected (or average) rate of return on stock is 10.5%
xxxx
k k Pi ii
N
(k )
1
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45Risk and Rates of ReturnRisk and Rates of Return
RiskRiskRisk is the uncertainty of future outcomes
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46Risk and Rates of ReturnRisk and Rates of Return
RiskRiskRisk is the uncertainty of future outcomes
ExampleExampleYou evaluate two investments: ElCat Corporation’s common stock and a one year Gov't Bond paying 6%. The return on the Gov't Bond does not depend on the state of the economy--you are guaranteed a 6% return.
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47Risk and Rates of ReturnRisk and Rates of Return
RiskRiskRisk is the uncertainty of future outcomes
ExampleExampleYou evaluate two investments: ElCat Corporation’s common stock and a one year Gov't Bond paying 6%. The return on the Gov't Bond does not depend on the state of the economy--you are guaranteed a 6% return.
100%
Return
Probability of Return
T-BillT-Bill
6%
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48Risk and Rates of ReturnRisk and Rates of Return
RiskRiskRisk is the uncertainty of future outcomes
ExampleExampleYou evaluate two investments: ElCat Corporation’s common stock and a one year Gov't Bond paying 6%. The return on the Gov't Bond does not depend on the state of the economy--you are guaranteed a 6% return.
100%
Return
Probability of Return
T-BillT-Bill
6%
10%Return
Probability of Return
ElCat CorpElCat Corp
5%
20%30%40%
–5% 10% 20%
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49Risk and Rates of ReturnRisk and Rates of Return
RiskRiskRisk is the uncertainty of future outcomes
ExampleExampleYou evaluate two investments: ElCat Corporation’s common stock and a one year Gov't Bond paying 6%. The return on the Gov't Bond does not depend on the state of the economy--you are guaranteed a 6% return.
100%
Return
Probability of Return
T-BillT-Bill
6%
10%Return
Probability of Return
ElCat CorpElCat Corp
5%
20%30%40%
–5% 10% 20%
There is risk in Owning ElCat stock, no risk in owning the Treasury Bill
There is risk in Owning ElCat stock, no risk in owning the Treasury Bill
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50Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
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51Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1
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52Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
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53Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
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54Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
x ( – 10.5%)2 = 24.025%2
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55Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xx
((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
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56Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxx
(((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
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57Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2– -- 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
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58Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
2 = 57.25%2
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59Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
2 = 57.25%2
= 57.25%2
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60Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
2 = 57.25%2
= 57.25%2
= 7.57%
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61Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
2 = 57.25%2
= 57.25%2
= 7.57%Higher standard deviation, higher riskHigher standard deviation, higher risk
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62Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
2 = 57.25%2
= 57.25%2
= 7.57%
NOTE:NOTE: The standard deviation of the T-Bill is 0%
NOTE:NOTE: The standard deviation of the T-Bill is 0%
Higher standard deviation, higher riskHigher standard deviation, higher risk
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63Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskMeasuring RiskStandard Deviation () measure the dispersion of
returns.
(k ) (k )i ii
N
k P2
1ExampleExampleCompute the standard deviation on ElCat common stock. the mean (k) was previously computed as 10.5%
State of Economy Probability Return
Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%
xxxx
((((
– 10.5%)2 = 24.025%2
– 10.5%)2 = 6.05%2
– 10.5%)2 = 0.10%2
– 10.5%)2 = 27.075%2
2 = 57.25%2
= 57.25%2
= 7.57%
Can compare the of 7.57 to another stock with expected return of 10.5%
Can compare the of 7.57 to another stock with expected return of 10.5%
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64Risk and Rates of ReturnRisk and Rates of Return
Measuring RiskStandard Deviation () for historical data can be used to measure the dispersion of historical returns.
N
ii kk
n 1
2)(_)1(
1
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65Risk and Rates of ReturnRisk and Rates of Return
Use the following data to calculate the historical return Use the following data to calculate the historical return of XYZof XYZ
YearYear ReturnReturn19921992 12%12%19931993 16%16%19941994 -8%-8%1995 6% 1995 6%
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66Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:
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67Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:Firm Specific Risk - Risk due to factors within the firm
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68Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:Firm Specific Risk - Risk due to factors within the firm
Stock price will most likely fall if a major government contract is discontinued unexpectedly.
Stock price will most likely fall if a major government contract is discontinued unexpectedly.
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69Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:Firm Specific Risk - Risk due to factors within the firmMarket related Risk - Risk due to overall market
conditions
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70Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:Firm Specific Risk - Risk due to factors within the firmMarket related Risk - Risk due to overall market
conditions
Stock price is likely to rise if overall stock market is doing well.
Stock price is likely to rise if overall stock market is doing well.
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71Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:Firm Specific Risk - Risk due to factors within the firmMarket related Risk - Risk due to overall market
conditionsDiversification: If investors hold stock of many
companies, the firm specific risk will be canceled out: Investors diversify portfolio.
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72Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two
parts:Firm Specific Risk - Risk due to factors within the firmMarket related Risk - Risk due to overall market
conditionsDiversification: If investors hold stock of many
companies, the firm specific risk will be canceled out: Investors diversify portfolio.
Firm specific risk also called diversifiable risk or unsystematic risk
Firm specific risk also called diversifiable risk or unsystematic risk
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73Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two parts:
Firm Specific Risk - Risk due to factors within the firmMarket related Risk - Risk due to overall market conditions
Diversification: If investors hold stock of many companies, the firm specific risk will be canceled out: Investors diversify portfolio.
Even if hold many stocks, cannot eliminate the market related risk
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74Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationRisk of a company's stock can be separated into two parts:
Firm Specific Risk - Risk due to factors within the firmMarket related Risk - Risk due to overall market conditions
Diversification: If investors hold stock of many companies, the firm specific risk will be canceled out: Investors diversify portfolio.
Even if hold many stocks, cannot eliminate the market related risk
Market related risk is also called non-diversifiable risk or systematic risk
Market related risk is also called non-diversifiable risk or systematic risk
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75Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationIf an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually eliminated
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76Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationIf an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually eliminated
Number of stocks in Portfolio
Variability of Returns
Market Related Risk
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77Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationIf an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually eliminated
Number of stocks in Portfolio
Variability of Returns
Firm Specific Risk
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78Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationIf an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually eliminated
Number of stocks in Portfolio
Variability of Returns
Total Risk
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79Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationIf an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually eliminated
Number of stocks in Portfolio
Variability of Returns
20
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80Risk and Rates of ReturnRisk and Rates of Return
Risk and DiversificationRisk and DiversificationIf an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually eliminated
Holding a general stock mutual fund (not a specific industry fund) is similar to holding a well-diversified portfolio.
Number of stocks in Portfolio
Variability of Returns
20
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81Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket risk is the risk of the overall market. To
measure the market risk we need to compare individual stock returns to the overall market returns.
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82Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket risk is the risk of the overall market. To
measure the market risk we need to compare individual stock returns to the overall market returns.
A proxy for the market is usually used: An index of stocks such as the S&P 500
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83Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket risk is the risk of the overall market, so to
measure need to compare individual stock returns to the overall market returns.
A proxy for the market is usually used: An index of stocks such as the S&P 500
Market risk measures how individual stock returns are affected by this market
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84Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket risk is the risk of the overall market, so to
measure need to compare individual stock returns to the overall market returns.
A proxy for the market is usually used: An index of stocks such as the S&P 500
Market risk measures how individual stock returns are affected by this market
Regress individual stock returns on Market index
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85Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskRegress individual stock returns on Market index
S&PReturn
PepsiCoReturn
-15% 15%-10% -5% 10%5%
5%
10%
15%
-5%
-10%
-15%
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86Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskRegress individual stock returns on Market index
S&PReturn
PepsiCoReturn
-15% 15%-10% -5% 10%5%
5%
10%
15%
-5%
-10%
-15%
Jan 1992PepsiCo -0.37%S&P -1.99%
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87Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskRegress individual stock returns on Market index
S&PReturn
PepsiCoReturn
-15% 15%-10% -5% 10%5%
5%
10%
15%
-5%
-10%
-15%
Plot Remaining Points
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88Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskRegress individual stock returns on Market index
S&PReturn
PepsiCoReturn
-15% 15%-10% -5% 10%5%
5%
10%
15%
-5%
-10%
-15%
Fit Regression Line
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89Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskRegress individual stock returns on Market index
S&PReturn
PepsiCoReturn
-15% 15%-10% -5% 10%5%
5%
10%
15%
-5%
-10%
-15%
Slope =riserun
5.5%5%
= = 1.1
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90Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket Risk is measured by Beta
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91Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket Risk is measured by BetaBeta is the slope of the characteristic line
S&PReturn
PepsiCoReturn
-15% 15%-10% -5% 10%5%
5%
10%
15%
-5%
-10%
-15%
Slope =riserun
5.5%5%
= = 1.1 = Beta ()
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92Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket Risk is measured by BetaBeta is the slope of the characteristic lineInterpreting Beta
Beta = 1Market Beta = 1Company with a beta of 1 has average risk
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93Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket Risk is measured by BetaBeta is the slope of the characteristic lineInterpreting Beta
Beta = 1Market Beta = 1Company with a beta of 1 has average risk
Beta < 1Low Risk CompanyReturn on stock will be less affected by the market than average
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94Risk and Rates of ReturnRisk and Rates of Return
Measuring Market RiskMeasuring Market RiskMarket Risk is measured by BetaBeta is the slope of the characteristic lineInterpreting Beta
Beta = 1Market Beta = 1Company with a beta of 1 has average risk
Beta < 1Low Risk CompanyReturn on stock will be less affected by the market than average
Beta > 1High Market Risk CompanyStock return will be more affected by the market than average
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95Risk and Rates of ReturnRisk and Rates of Return
RequiredRate ofReturn
Minimum rate of return necessary to attract investors to buy funds=
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96Risk and Rates of ReturnRisk and Rates of Return
RequiredRate ofReturn
Minimum rate of return necessary to attract investors to buy funds=
Required rate of return, K, depends on the risk-free rate(Krf) and the risk premium(Krp)
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97Risk and Rates of ReturnRisk and Rates of Return
RequiredRate ofReturn
Minimum rate of return necessary to attract investors to buy funds=
Required rate of return, K, depends on the risk-free rate(Krf) and the risk premium(Krp)
Using the capital asset pricing model (CAPM) the risk premium(Krp) depends on market risk
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98Risk and Rates of ReturnRisk and Rates of Return
RequiredRate ofReturn
Minimum rate of return necessary to attract investors to buy funds=
Required rate of return, K, depends on the risk-free rate(Krf) and the risk premium(Krp)
Using the capital asset pricing model (CAPM) the risk premium(Krp) depends on market risk
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
where:Kj = required rate of return on the jth securityj = Beta for the jth security
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99Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
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100Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
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101Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%Risk Free Rate
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102Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%
12%
Risk & Returnon market
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103Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%
SML
Connect Points forSecurity Market Line
Market
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104Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%
SMLIf of security j =1.2
Market
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105Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%
SMLIf of security j =1.2
1.2
Market
j
Kj = 5%+1.2(12% – 5%)
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106Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%
SMLIf of security j =1.2
1.2
13.4%
Market
j
Kj = 5%+1.2(12% – 5%)=13.4%
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107Risk and Rates of ReturnRisk and Rates of Return
Example:Example:If the expected return on the market is 12% and the risk free rate is 5%:
Kj = 5% + j (12% – 5% )
Kj = Krf + j ( Km – Krf )
Security Market LineSecurity Market Line
Beta1.51.0.50
15%
10%
5%
SMLIf of security j =1.2
1.2
13.4%
Market
j
Kj = 5%+1.2(12% – 5%)=13.4%
If = 1.2, investors will require a 13.4% return on the stock
If = 1.2, investors will require a 13.4% return on the stock
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108Risk and Rates of Return Risk and Rates of Return
ki : Expected (or required) rate of return from an ki : Expected (or required) rate of return from an investment i.investment i.
KRF : Risk free rate of return (e.g., 3 moth T-Bill rate)KRF : Risk free rate of return (e.g., 3 moth T-Bill rate)kM : Expected return from a market (e.g., S&P500) kM : Expected return from a market (e.g., S&P500)
portfolioportfolio(kM - kRF) : Market Risk Premium(kM - kRF) : Market Risk Premium(kM - kRF) : Risk Premium on asset i(kM - kRF) : Risk Premium on asset i
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109Risk and Rates of ReturnRisk and Rates of Return
Portfolio Return = Portfolio Return = w wii x k x kii
Return of a portfolio is the weighted average return of Return of a portfolio is the weighted average return of individual securities in the portfolio.individual securities in the portfolio.
Portfolio beta = Portfolio beta = w wii x x ii
Beta of a portfolio is the weighted average beta of Beta of a portfolio is the weighted average beta of individual securities in the portfolio.individual securities in the portfolio.