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Chapter 5 Chapter 5

Risk and Risk and

Return Return

Risk and Risk and

Return Return

Risk and ReturnRisk and Return Risk and Return

Risk and Return

 (^) Defining Risk and Return  (^) Using Probability Distributions to Measure Risk  (^) Attitudes Toward Risk  (^) Risk and Return in a Portfolio Context  (^) Diversification  (^) The Capital Asset Pricing Model (CAPM)  (^) Defining Risk and Return  (^) Using Probability Distributions to Measure Risk  (^) Attitudes Toward Risk  (^) Risk and Return in a Portfolio Context  (^) Diversification  (^) The Capital Asset Pricing Model (CAPM)

Return ExampleReturn Example Return Example

Return Example

The stock price for Stock A was $10$10 per share 1 year ago. The stock is currently trading at $9.50$9.50 per share, and shareholders just received a $1 dividend$1 dividend. What return was earned over the past year? The stock price for Stock A was $10$10 per share 1 year ago. The stock is currently trading at $9.50$9.50 per share, and shareholders just received a $1 dividend$1 dividend. What return was earned over the past year?

Return ExampleReturn Example Return Example

Return Example

The stock price for Stock A was $10$10 per share 1 year ago. The stock is currently trading at $9.50$9.50 per share, and shareholders just received a $1 dividend$1 dividend. What return was earned over the past year? The stock price for Stock A was $10$10 per share 1 year ago. The stock is currently trading at $9.50$9.50 per share, and shareholders just received a $1 dividend$1 dividend. What return was earned over the past year?

RR = = 5%5%

Determining Expected Determining Expected

Return (Discrete Dist.) Return (Discrete Dist.)

Determining Expected Determining Expected

Return (Discrete Dist.) Return (Discrete Dist.)

R =  ( R

i )( P i )

R is the expected return for the asset,

Ri is the return for the i

th

possibility,

P

i

is the probability of that return

occurring,

n is the total number of possibilities.

R =  ( R

i )( P i )

R is the expected return for the asset,

Ri is the return for the i

th

possibility,

P

i

is the probability of that return

occurring,

n is the total number of possibilities.

n i=

How to Determine the Expected How to Determine the Expected

Return and Standard Deviation Return and Standard Deviation

How to Determine the Expected How to Determine the Expected

Return and Standard Deviation Return and Standard Deviation

Stock BW Ri Pi (Ri)(Pi) -.15 .10 -. -.03 .20 -. .09 .40. .21 .20. .33 .10. Sum 1.00 .090. Stock BW Ri Pi (Ri)(Pi) -.15 .10 -. -.03 .20 -. .09 .40. .21 .20. .33 .10. Sum 1.00 .090. The expected return, R, for Stock BW is. or 9%

How to Determine the Expected How to Determine the Expected

Return and Standard Deviation Return and Standard Deviation

How to Determine the Expected How to Determine the Expected

Return and Standard Deviation Return and Standard Deviation

Stock BW Ri Pi (Ri)(Pi) (Ri - R )^2 (Pi) -.15 .10 -.015. -.03 .20 -.006. .09 .40 .036. .21 .20 .042. .33 .10 .033. Sum 1.00 .090.090 .01728. Stock BW Ri Pi (Ri)(Pi) (Ri - R )^2 (Pi) -.15 .10 -.015. -.03 .20 -.006. .09 .40 .036. .21 .20 .042. .33 .10 .033. Sum 1.00 .090.090 .01728.

Determining Standard Determining Standard

Deviation (Risk Measure) Deviation (Risk Measure)

Determining Standard Determining Standard

Deviation (Risk Measure) Deviation (Risk Measure)

  =  ( Ri - R )

2 ( Pi )

  = .1315.1315 or 13.15%13.15%

  =  ( Ri - R )

2 ( Pi )

  = .1315.1315 or 13.15%13.15%

n i=

Discrete vs. Continuous Discrete vs. Continuous

Distributions Distributions

0

-15% -3% 9% 21% 33% Discrete Continuous 0

-50% -41% -32% -23% -14% -5%^ 4% 13% 22% 31% 40% 49% 58% 67%

Determining Expected Determining Expected

Return (Continuous Dist.) Return (Continuous Dist.)

Determining Expected Determining Expected

Return (Continuous Dist.) Return (Continuous Dist.)

R =  ( R

i ) / ( n )

R is the expected return for the asset,

Ri is the return for the ith observation,

n is the total number of observations.

R =  ( R

i ) / ( n )

R is the expected return for the asset,

Ri is the return for the ith observation,

n is the total number of observations.

n i=

Continuous Continuous

Distribution Problem Distribution Problem

 (^) Assume that the following list represents the continuous distribution of population returns for a particular investment (even though there are only 10 returns).  (^) 9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5%  (^) Calculate the Expected Return and Standard Deviation for the population assuming a continuous distribution.

Certainty Equivalent Certainty Equivalent ( CECE ) is the

amount of cash someone would

require with certainty at a point in

time to make the individual

indifferent between that certain

amount and an amount expected to

be received with risk at the same

point in time.

Certainty Equivalent Certainty Equivalent ( CECE ) is the

amount of cash someone would

require with certainty at a point in

time to make the individual

indifferent between that certain

amount and an amount expected to

be received with risk at the same

point in time.

Risk AttitudesRisk Attitudes Risk Attitudes

Risk Attitudes

Risk Attitude Example Risk Attitude Example

You have the choice between (1) a guaranteed dollar reward or (2) a coin-flip gamble of $100,000 (50% chance) or $0 (50% chance). The expected value of the gamble is $50,000.  (^) Mary requires a guaranteed $25,000, or more, to call off the gamble.  (^) Raleigh is just as happy to take $50,000 or take the risky gamble.  (^) Shannon requires at least $52,000 to call off the gamble.

What are the Risk Attitude tendencies of each?What are the Risk Attitude tendencies of each?

Risk Attitude ExampleRisk Attitude Example Risk Attitude Example

Risk Attitude Example

Mary shows “risk aversion”“risk aversion” because her “certainty equivalent” < the expected value of the gamble.. Raleigh exhibits “risk indifference”“risk indifference” because her “certainty equivalent” equals the expected value of the gamble.. Shannon reveals a “risk preference”“risk preference” because her “certainty equivalent” > the expected value of the gamble.. Mary shows “risk aversion”“risk aversion” because her “certainty equivalent” < the expected value of the gamble.. Raleigh exhibits “risk indifference”“risk indifference” because her “certainty equivalent” equals the expected value of the gamble.. Shannon reveals a “risk preference”“risk preference” because her “certainty equivalent” > the expected value of the gamble..