Lesson 6 of 7 · All lessons in this module
  1. Portfolio expected return and varianceVideo lesson
  2. Covariance and correlation
  3. The covariance matrix and many-asset portfolios
  4. Correlation and diversification
  5. Covariance from a joint probability function
  6. Shortfall risk and Roy's safety-first criterion
  7. Shortfall probability, the Sharpe ratio and VaR

Lesson 6 of 7 · 13 min

Shortfall risk and Roy's safety-first criterion

If the investor's main fear is ending below a minimum return, choose the portfolio with the highest safety-first ratio: the most standard deviations between the expected return and the threshold.

In short

  • Mean–variance analysis treats upside and downside variability alike; safety-first rules focus on the downside.
  • Shortfall risk: the risk that portfolio value or return falls below a minimum acceptable level over a given horizon.
  • Roy's safety-first criterion: choose the portfolio that minimises P(Rp<RL)P(R_p < R_L), where RLR_L is the threshold return.
  • With normal returns this means maximising the safety-first ratio: SFRatio=[E(Rp)−RL]/σp\text{SFRatio} = [E(R_p) - R_L]/\sigma_p.
  • Method: compute each portfolio's SFRatio, pick the highest. The threshold often comes from a planned withdrawal ÷ portfolio value.

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