36 Questions
Which term contributes the most to the portfolio variance?
$2(0.50)(0.25)(189)$
What is the standard deviation of return for the portfolio?
14%
What is the expected annual return of the portfolio?
11.75%
What is the sum of the first three terms in the calculation?
132.625
If the returns on the three assets were independent, what would be the standard deviation of portfolio return?
11.52%
What is the risk reduction benefit from holding a portfolio of assets called?
Diversification benefit
What is the key insight of modern portfolio theory?
Diversification benefit
What would happen to portfolio variance and risk if the covariance terms were negative?
They would decrease
What does the diversification benefit increase with?
Decreasing covariance
What concept is even more intuitively stated when discussing the diversification benefit?
Correlation benefit
Which of the following is used as a measure of reward in modern portfolio theory?
Expected return
What is the expected return on a portfolio?
A weighted average of the expected returns on the securities in the portfolio
Which equation represents the calculation of portfolio expected return?
$E(Rp) = w1E(R1) + w2E(R2) + …+wnE(Rn)$
What is the formula for portfolio variance of return?
$σ2(Rp) = E{[RpE(Rp)]2}$
Which equation is used to calculate the expected return on the portfolio in the given example?
$E(Rp) = 0.50(13%) + 0.25(6%) + 0.25(15%)$
What is used as a measure of investment risk in modern portfolio theory?
Portfolio variance of return
What is the formula for portfolio variance in a forward-looking sense?
$σ2(Rp) = E{[RpE(Rp)]2}$
What are the weights used in the calculation of portfolio expected return?
The respective proportions of the portfolio in currency units
What is the measure of risk used in modern portfolio theory?
Variance of return
What is the equation for portfolio expected return?
$E(Rp) = w1E(R1) + w2E(R2) + …+wnE(Rn)$
Which equation represents the covariance between two random variables Ri and Rj?
Cov(Ri ,Rj) = E[(Ri − ERi)(Rj − ERj)]
What is the formula for the sample covariance between two random variables Ri and Rj?
Cov(Ri ,Rj) = ∑n=1 n (Ri,t , _ R i)(Rj,t − E _ R j) ⁄ (n − 1)
What is the equation for the variance of a three-asset portfolio?
σ2(Rp) = w12σ2(R1) + w1w2Cov(R1,R2) + w1w3Cov(R1,R3) +w1w2Cov(R1,R2) + w22σ2(R2) + w2w3Cov(R2,R3) +w1w3Cov(R1,R3) + w2w3Cov(R2,R3) + w23σ2(R3)
What is the most compact way to state Equation 5, which represents the variance of a portfolio?
σ2(Rp) = ∑i=1 3 ∑j=1 3 wiwjCov(Ri ,Rj)
What is the general equation for the variance of a portfolio of any size n?
σ2(Rp) = ∑i=1 n ∑j=1 n wiwjCov(Ri ,Rj)
What does covariance measure?
How the co-movements of returns affect aggregate portfolio variance
Which equation represents the calculation of portfolio variance in a forward-looking sense?
$\sigma^2(R_p) = \sum_{i=1}^3 \sum_{j=1}^3 w_i w_j Cov(R_i, R_j)$
Which term contributes the most to the portfolio variance?
The covariance terms
What is the measure of risk used in modern portfolio theory?
Standard deviation
What is the expected annual return of the portfolio?
$E(R_p)$
What are the weights used in the calculation of portfolio expected return?
$w_1, w_2, w_3$
What is the key insight of modern portfolio theory?
Diversification can reduce risk
What is the formula for portfolio variance of return?
$\sigma^2(R_p) = \sum_{i=1}^3 \sum_{j=1}^3 w_i w_j Cov(R_i, R_j)$
What is used as a measure of investment risk in modern portfolio theory?
Standard deviation
What is the standard deviation of return for the portfolio?
$\sigma(R_p)$
What is the equation for portfolio expected return?
$E(R_p) = w_1 E(R_1) + w_2 E(R_2) + w_3 E(R_3)$
Study Notes
Portfolio Variance and Risk
- The covariance term contributes the most to the portfolio variance.
- The standard deviation of return for the portfolio is a measure of investment risk.
- The expected annual return of the portfolio is the sum of the weighted returns of individual assets.
Modern Portfolio Theory
- The key insight of modern portfolio theory is that the risk of a portfolio can be reduced through diversification.
- Diversification benefit increases with the number of assets in the portfolio.
- The concept of diversification benefit is more intuitively stated when discussing the risk reduction benefit of holding a portfolio.
Portfolio Return and Variance
- The expected return on a portfolio is the sum of the weighted returns of individual assets.
- The formula for portfolio variance of return is: variance = w1^2 * σ1^2 + w2^2 * σ2^2 + w3^2 * σ3^2 + 2 * w1 * w2 * σ1 * σ2 + 2 * w1 * w3 * σ1 * σ3 + 2 * w2 * w3 * σ2 * σ3.
- The formula for portfolio variance in a forward-looking sense is: variance = w1^2 * σ1^2 + w2^2 * σ2^2 + w3^2 * σ3^2 + 2 * w1 * w2 * σ1 * σ2 + 2 * w1 * w3 * σ1 * σ3 + 2 * w2 * w3 * σ2 * σ3.
- The equation for portfolio expected return is: E(Rp) = w1 * E(R1) + w2 * E(R2) + w3 * E(R3).
- The weights used in the calculation of portfolio expected return are the proportions of each asset in the portfolio.
Covariance and Risk
- Covariance measures the linear relationship between two random variables.
- The formula for the sample covariance between two random variables Ri and Rj is: cov(Ri, Rj) = Σ{(Ri - E(Ri)) * (Rj - E(Rj))} / (n - 1).
- The equation for the variance of a three-asset portfolio is: variance = w1^2 * σ1^2 + w2^2 * σ2^2 + w3^2 * σ3^2 + 2 * w1 * w2 * σ1 * σ2 + 2 * w1 * w3 * σ1 * σ3 + 2 * w2 * w3 * σ2 * σ3.
- The general equation for the variance of a portfolio of any size n is: variance = Σ{wi^2 * σi^2} + 2 * Σ{wi * wj * σi * σj}.
Risk Reduction
- If the returns on the three assets were independent, the standard deviation of portfolio return would be lower.
- If the covariance terms were negative, portfolio variance and risk would decrease.
- The measure of risk used in modern portfolio theory is standard deviation.
Test your knowledge of portfolio return and risk metrics with this quiz. Explore the concepts of expected return and variance of return in modern portfolio theory.
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