Reading 42: Portfolio Risk and Return Pt 1

Question 1

Holding Period Return

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Portfolio Risk and Return Pt 1

Answer 1

Question 2

Annualized Return

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Portfolio Risk and Return Pt 1

Answer 2

c is the number of periods in a year

Question 3

Portfolio Return with 2 Assets (weighted)

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Portfolio Risk and Return Pt 1

Answer 3

Question 4

Relationship Between Nominal and Real Return

(3 equations)

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Portfolio Risk and Return Pt 1

Answer 4

r = nominal return

r_rF = a real risk-free return as compensation for postponing consumption

π = inflation as compensation for loss of purchasing power

RP = risk premium for assuming risk

Question 5

Variance of a Single Asset

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Portfolio Risk and Return Pt 1

Answer 5

Rt = return for period t

T = total number of periods

µ = mean of T returns, assuming T is the population of returns

Question 6

Sample Variance of a Single Asset

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Portfolio Risk and Return Pt 1

Answer 6

Rt = return for period t

T - 1 = use for sample number of periods

R bar = mean return of sample observations

s² = sample varianec

Question 7

Population and sample standard deviation

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Portfolio Risk and Return Pt 1

Answer 7

Question 8

General Expression of Portfolio Variance for N Securities

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Portfolio Risk and Return Pt 1

Answer 8

Question 9

Porfolio Variance Separating Covariances

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Portfolio Risk and Return Pt 1

Answer 9

Because the covariance of an asset with itself is the variance of the asset, we can separate the variances from the covariances in the second equation.

Cov(Ri,Rj) is the covariance of returns, Ri and Rj, and can be expressed as the product of the correlation between the two returns(Þ_1,2) and the standard deviations of the two assets. Thus, Cov (R_i,R_j) = Þ_ijσ_iσ_j

Question 10

Two asset portfolio variance simplification using covariance and then using correlation

42.x

Portfolio Risk and Return Pt 1

Answer 10

Question 11

Two asset portfolio standard deviation from variance simplification using covariance and then using correlation

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Portfolio Risk and Return Pt 1

Answer 11

Question 12

Relationship between the expected return and the real risk-free interest rate, inflation rate, and risk premium

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Portfolio Risk and Return Pt 1

Answer 12

Question 13

Example of Utility Function

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Portfolio Risk and Return Pt 1

Answer 13

U is the utility of the investment

E(r) is the expected return

σ² is the variance

Question 14

Standard Deviation for a Portfolio of Two Assets when One Asset is the Risk-Free Asset

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Portfolio Risk and Return Pt 1

Answer 14

Question 15

Equation for Capital Allocation Line

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Portfolio Risk and Return Pt 1

Answer 15

w₁ = 1 - (σ_p / σ_i)

That is the substitute into the expected return equation

Question 16

Usable Form for Equation for Capital Allocation Line

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Portfolio Risk and Return Pt 1

Answer 16

Slope Intercept

Question 17

Portfolio of Many Risky Assets (expanded; base)

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Portfolio Risk and Return Pt 1

Answer 17

Question 18

Portfolio of Many Risky Assets (simplified)

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Portfolio Risk and Return Pt 1

Answer 18

Question 19

Portfolio of Many Risky Assets (assuming all assets have same variance and the same correlation among assets)

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Portfolio Risk and Return Pt 1

Answer 19

Question 20

General rule to evaluate whether a new asset should be included to an existing portfolio

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Portfolio Risk and Return Pt 1

Answer 20

Question 21

If a new asset should be included in portfolio Sharpe Ratio

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Portfolio Risk and Return Pt 1

Answer 21

If the Sharpe ratio of the new asset is greater than the Sharpe ratio of the current portfolio times the correlation coefficient, it is beneficial to add the new asset.