Question 37 of 50

Given three assets with weights 0.4, 0.3, and 0.3, individual variances 100, 81, and 144 (in % squared) and covariances Cov12=20, Cov13=10, Cov23=30 (all in % squared), what is the portfolio variance (in % squared)?

If two assets have standard deviations of 10% and 20% and their covariance is 12 (% squared), what is the correlation between them?

Portfolio expected return for a portfolio with weights 0.5 in Asset A (E[R]=8%) and 0.5 in Asset B (E[R]=12%) is:

If two assets are independent, which statement is always true?

Given joint probabilities of two assets across three states: P(state1)=0.2 with (R_A=25%, R_B=20%); state2 P=0.5 with (12%,16%); state3 P=0.3 with (10%,10%). The expected returns are 14% for A and 15% for B. What is Cov(RA,RB)?

A portfolio has expected return 12%, standard deviation 15%. Investor's minimum acceptable return RL is 3%. What is the safety-first ratio?

If RL equals the risk-free rate, what classic performance ratio is equivalent to Roy's safety-first ratio?

For a covariance matrix of three assets given as variances on diagonal [400, 81, 441] and covariances [45, 189, 38] corresponding to Cov(S&P, Bonds)=45, Cov(S&P, EAFE)=189, Cov(Bonds, EAFE)=38 (units percent squared), and weights 0.5, 0.25, 0.25, which portfolio standard deviation (approx) results?

If two assets have covariance 0 and nonzero variances, what is their correlation?

A two-asset portfolio has weights 0.3 and 0.7, standard deviations 12% and 25%, and correlation 0.2. What is the portfolio standard deviation (approx)?

How many distinct covariance terms must be estimated for a portfolio of 20 assets (excluding variances)?

If a portfolio's covariances with other holdings are largely negative, what effect does this have on portfolio variance all else equal?

Using a joint probability table, why is covariance calculated by summing P(Ri, Rj)*(Ri - E(Ri))*(Rj - E(Rj)) across all cells?

A fund has expected return 6% and standard deviation 9%. The minimum acceptable return RL is 2%. What is approximate probability the fund returns below 2% if returns are normal? (Use Normal table: N(-0.444)~0.328.)

In the 3-asset covariance matrix example, if all off-diagonal covariances were set to zero, the portfolio standard deviation would be smaller. This illustrates:

Which of the following statements about correlation is correct?

If you increase the number of independent holdings in a portfolio (with identical individual variances and near-zero covariances), what happens to portfolio variance?

Given a covariance matrix entry Cov(Ri,Rj)=0.20 (in decimal return units), sigma_i=0.10 and sigma_j=0.25, what is corr(Ri,Rj)?

Which term increases in importance for portfolio variance as the number of assets increases (assuming nonzero correlations)?

If two assets have a correlation of -1, what is the implication for a portfolio constructed as a weighted combination of the two (ignoring leverage limitations)?

You estimate expected returns for three assets as 13%, 6%, and 15% and set weights 0.50, 0.25, 0.25. What is expected portfolio return?

Which of the following is true about covariance signs?

If portfolio variance equals 195.875 (% squared) what is standard deviation (percent)?

What is covariance if correlation is 0.25 and standard deviations are 8.2% and 3.4% (use percent units)?

Which of the following best describes Roy's safety-first criterion?

If expected return on portfolio A is 25% with sd 27% and portfolio B is 11% with sd 8% and RL=3.75%, which has lower shortfall probability?

Given covariance matrix entry Cov(S&P, EAFE)=189 (%^2), S&P variance=400, EAFE variance=441, what is correlation between S&P and EAFE?

Covariance between two assets is negative. Which statement is true?

You have a portfolio with expected return 8% and standard deviation 8%. RL for investor is 2%. Which probability (approx) of shortfall applies? (z=(2-8)/8=-0.75; Normal(-0.75)=0.2266).

In computing portfolio variance using a covariance matrix, why can we use only the upper (or lower) triangular covariances plus diagonal variances instead of all n^2 entries?

When constructing a two-asset plot of portfolio expected return vs standard deviation as weights change from all in asset 1 to all in asset 2, the shape is typically:

If the covariance between portfolio returns and bond index returns is +18.9 (percent squared) and both series have positive standard deviations, the correlation is:

Which of the following is true about the safety-first ratio and the probability of shortfall under normal returns?

In Example 3, when comparing portfolio variances before and after a regulation change with sample variances 4.644 and 3.919 over equal sample sizes (418), the F-statistic was 1.185. If the two-tailed critical interval is (0.8251,1.2119), what is the inference?

A portfolio manager says 'if we diversify across many securities, portfolio risk will approach zero.' The correct response is:

Which numeric operation yields a portfolio's expected return from component expected returns and weights?

If portfolio expected return equals weighted sum of expected returns, which input change will NOT change expected portfolio return?

A covariance estimate between two assets is negative. To improve overall portfolio variance, an investor should:

You compute portfolio variance using percent units. Why is it important to be consistent with percent vs decimal usage?

If two assets have expected returns 5% and 9% and weights 0.6 and 0.4, what is the portfolio expected return?

Which of the following components of portfolio variance grows most rapidly as number of assets increases?

In a joint probability function with mutually exclusive states that sum to 1, how do you compute E(R) for a single asset?

When using a covariance matrix expressed in percent squared, portfolio variance computed with percent-based weights yields result in:

What is a practical reason portfolio managers prefer stratified sampling for bond index replication rather than pure simple random sampling?

A portfolio has expected return 6% and sd 10%. If investor wants 99% confidence that return >= RL, what RL approximately equals? (z for 99% one-sided is 2.33 so RL = E - z*sigma = 6% - 2.33*10% = -16.3%)

If portfolio A has SFratio 0.5 and portfolio B has SFratio 0.8 under normality, which has lower probability of falling below RL?

Which is the correct formula for portfolio variance in matrix notation using weight vector w and covariance matrix Sigma?

Which action would increase the SFratio for a portfolio (all else equal)?

Practical recommendation: when estimating a large covariance matrix for 50 assets using historical returns, an analyst should: