Examen 2. Etapa 3 Quantitative Methods

ESN stock has a variance of 0.30 and PNX stock has a variance of 0.18. If the covariance between the two stocks is -0.09, their correlation is closest to:

A client holding a $2,500,000 portfolio wants to avoid withdrawing more than $90,000 in one year from principal, implying a shortfall threshold return of 3.6%. Using Roy’s safety-first criterion, which allocation is optimal? Allocation A: expected return 6.0%, standard deviation 7.80%. Allocation B: expected return 8.0%, standard deviation 11.20%. Allocation C: expected return 9.5%, standard deviation 15.60%.

A diversified portfolio has an expected return of 7% and a standard deviation of 9%. If an investor’s minimum acceptable (threshold) return is -5%, the safety-first ratio is closest to:

A portfolio holds six stocks with the following one-year total returns and beginning market values: 10.1% on $180,000; 12.8% on $120,000; -5.5% on $160,000; 14.2% on $350,000; 16.5% on $90,000; and -8.2% on $200,000. The portfolio return over the period is closest to:

For a portfolio of six assets, the number of unique covariance terms (excluding the variances) required to compute the portfolio return variance is:

US and Spanish sovereign bonds have return standard deviations of 0.58 and 0.50, respectively. If the correlation between their returns is 0.30, the covariance of returns is closest to:

All else equal, as the correlation between the returns of two assets in a portfolio approaches +1.0, the diversification benefit most likely:

Which of the following is a key advantage of bootstrap resampling over a purely analytical (closed-form) approach to estimating a statistic’s standard error?

An analyst prices a complex path-dependent option whose payoff has no closed-form solution. She specifies a distribution for the underlying asset’s returns and runs 10,000 simulated price paths. This procedure is best described as:

A Monte Carlo simulation of a portfolio’s terminal value is run with 500 trials and then rerun with 50,000 trials. Increasing the number of trials will most likely:

Which statement best contrasts Monte Carlo simulation with historical simulation?

An analyst regresses a company’s return on equity (ROE, in percent) on its three-year sales growth rate (GRW, in percent) over 24 years and obtains an estimated regression of ROE = 4.6 + 1.55(GRW). For a firm with a sales growth rate of 9 percent and an observed ROE of 22 percent, the residual is closest to:

An analyst’s ANOVA output for a simple linear regression shows a regression (explained) sum of squares of 0.0335 and a total sum of squares of 0.0442. The coefficient of determination for this regression is closest to:

A simple linear regression of a stock’s return on its benchmark’s return produces a coefficient of determination of 0.6842. Given that the estimated slope coefficient is positive, the correlation between the two return series is closest to:

An analyst reports the following ANOVA results for a simple linear regression estimated with 48 observations: regression sum of squares of 42.15 (1 degree of freedom) and residual sum of squares of 360.22 (46 degrees of freedom). The F-statistic for the overall significance of the regression is closest to:

In a simple linear regression, the estimated slope coefficient is -3.885 with a standard error of 1.642. The t-statistic for testing whether the slope coefficient differs from zero is closest to:

An analyst regresses the monthly returns of the Halcyon Growth Fund on the monthly returns of a market index to estimate the fund’s beta. The standard deviation of the index return is 1.24%, the standard deviation of the fund return is 2.05%, and the correlation between the two return series is -0.588. The estimated slope coefficient (beta) is closest to:

An analyst estimates a simple linear regression of a fund’s monthly return on a market index’s monthly return. The mean index return is 0.82%, the mean fund return is 1.05%, the standard deviation of the index return is 1.20%, the standard deviation of the fund return is 1.85%, and the correlation between them is -0.560. The estimated intercept (alpha) of the regression is closest to:

An analyst produces a point forecast Yf from a simple linear regression and computes the standard error of the forecast to be 0.0512. Using a 99% confidence level, the appropriate two-sided critical t-value is 2.712. The 99% prediction interval for the forecast is best described as:

In a simple linear regression with one independent variable, the estimated slope coefficient is 1.4520 with a standard error of 0.2140. The F-statistic for testing the overall significance of the regression is closest to: