Apply Portfolio Analysis Concepts - Series 7

Which risk can be reduced substantially through diversification?

Unsystematic (company-specific) risk. Diversification mitigates risks specific to individual companies or industries by spreading investments across various assets.
Calculate $R_p$ if $50\%$ earns $10\%$ and $50\%$ earns $-2\%$ in the same period.

$4\%$ . Portfolio return is computed as the weighted average of the realized returns from its constituent investments.
Which term describes the risk reduction achieved by combining imperfectly correlated assets?

Diversification benefit (risk reduction from correlation below $+1$ ). Combining assets with correlation less than +1 reduces portfolio risk below the weighted average of individual risks.
What is the key difference between systematic risk and unsystematic risk?

Systematic affects all markets; unsystematic is issuer/industry-specific. Systematic risk impacts the entire market and cannot be diversified away, whereas unsystematic risk is unique to specific entities and can be reduced through diversification.
What does correlation measure between two investments?

The degree to which their returns move together. Correlation quantifies the linear relationship between asset returns, influencing the effectiveness of diversification in a portfolio.
What does a correlation of $+1$ between two assets imply for diversification?

No diversification benefit; returns move perfectly together. Perfect positive correlation indicates assets fluctuate identically, eliminating any risk reduction from combining them.
State the formula for portfolio variance for two assets using correlation.

$\sigma_p^2=w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\sigma_1\sigma_2\rho_{12}$ . Portfolio variance incorporates the weighted variances of assets and their covariance, adjusted by the correlation coefficient.
What does the Sharpe ratio measure?

Risk-adjusted return using total risk (standard deviation). The Sharpe ratio assesses excess return per unit of total risk, facilitating comparison of investments' efficiency.
What does a beta of $1.2$ indicate about a stock's market risk?

It is $20\%$ more volatile than the market (systematic risk). A beta exceeding 1 signifies greater sensitivity to market fluctuations, amplifying systematic risk relative to the market.
Identify the portfolio result when a holding grows and exceeds its target weight.

Allocation drift (the portfolio becomes overweight that holding). Uneven performance among assets causes their proportions to shift from original targets, leading to unintended risk exposure.
What is asset allocation in portfolio analysis?

Choosing weights among asset classes to meet risk/return objectives. Asset allocation involves strategically distributing investments across categories to align with an investor's goals for risk and return.
Which option best defines alpha ( $\alpha$ ) in performance evaluation?

Return above or below the return predicted by market risk (beta). Alpha measures the excess return generated beyond what is expected based on the security's beta and market performance.
Which option best describes the effect of lowering correlation on portfolio volatility?

Lower correlation generally lowers portfolio volatility, holding else constant. Reducing correlation enhances diversification, decreasing overall portfolio risk for given asset volatilities and weights.
What is rebalancing in the context of asset allocation?

Restoring portfolio weights to target allocations after drift. Rebalancing adjusts asset weights back to strategic targets to maintain the intended risk-return profile over time.
Which correlation value provides the greatest diversification benefit?

A correlation of $-1$ . Perfect negative correlation means assets move in opposite directions, maximizing risk reduction when combined in a portfolio.
State the relationship between portfolio variance and standard deviation.

$\sigma_p=\sqrt{\sigma_p^2}$ . Portfolio standard deviation is derived as the square root of portfolio variance to express risk in the same units as returns.
State the formula for the Sharpe ratio.

$S=\frac{R_p-R_f}{\sigma_p}$ . The Sharpe ratio computes the portfolio's return premium over the risk-free rate divided by its standard deviation.
Which risk cannot be eliminated by diversification, even with many holdings?

Systematic (market) risk. Systematic risk is inherent to the market as a whole and persists regardless of the number of assets held in a portfolio.
Which option best defines diversification in portfolio analysis?

Spreading investments across assets to reduce unsystematic risk. Diversification reduces exposure to any single asset's performance by distributing investments, thereby mitigating unsystematic risk.
What is the standard deviation of returns commonly used to measure?

Volatility (total risk) of an investment's returns. Standard deviation quantifies the dispersion of returns around the mean, serving as a measure of an investment's overall risk.
State the formula for expected return of a two-asset portfolio.

$E(R_p)=w_1E(R_1)+w_2E(R_2)$ . The expected portfolio return is calculated as the weighted sum of the individual assets' expected returns.
Which factor most directly drives an investor's appropriate asset allocation?

Risk tolerance and time horizon. An investor's ability to withstand losses and the investment period determine the suitable mix of assets to balance risk and potential returns.
Which option best defines beta ( $\beta$ ) as used in portfolio analysis?

Sensitivity of a security's return to market movements. Beta quantifies how a security's returns respond to changes in the overall market return.
Identify the higher-volatility investment if $\sigma_A=12\%$ and $\sigma_B=18\%$ .

Investment $B$ . Higher standard deviation reflects greater dispersion in returns, indicating increased volatility and risk.
Calculate $E(R_p)$ for $w_1=0.60$ , $E(R_1)=8\%$ , $w_2=0.40$ , $E(R_2)=4\%$ .

$6.4\%$ . The expected portfolio return is the weighted average of the component assets' expected returns.

Study these flashcards