Priya, aged 46, holds her entire investment portfolio in three technology shares accumulated through her employer's share purchase plan. She asks her planner which single statistic best captures the total risk she is currently bearing on that portfolio. Which measure should the planner use?
- ABeta, because beta scales the portfolio's return volatility to that of the broad market and so expresses the risk she is bearing in a single comparable figure.
- BThe average correlation coefficient between the three shares, because correlation is what determines how much risk a concentrated holding carries.
- CThe Sharpe ratio, because it converts the portfolio's excess return into one figure that expresses the risk she is taking on.
- DStandard deviation, because a portfolio that is not diversified still carries substantial unsystematic risk and standard deviation measures total risk, systematic plus unsystematic. Correct
Why A is wrong: Tempting because beta is the most familiar risk statistic and it does produce one comparable number. It is wrong here because beta measures systematic risk alone. Priya's dominant exposure is company specific, so beta would understate the risk she actually carries.
Why B is wrong: Tempting because correlation genuinely drives diversification benefit. It is wrong because correlation is an input to a risk calculation rather than a measure of magnitude. A correlation figure alone says nothing about how far her returns can swing.
Why C is wrong: Tempting because the Sharpe ratio contains standard deviation in its denominator. It is wrong because it reports return per unit of risk, not the amount of risk. Two portfolios with very different volatility can share a Sharpe ratio.
Why D is correct: Correct. Standard deviation measures the dispersion of the portfolio's own returns, which for a three share concentrated holding is driven largely by company specific events. Because unsystematic risk has not been diversified away, total risk is the relevant quantity and standard deviation is the measure of it.