Lessons

- What is a Probability Distribution
- Discrete Vs. Continuous Random Variable
- Cumulative Distribution Function
- Discrete Uniform Random Variable
- Bernoulli and Binomial Distribution
- Stock Price Movement Using a Binomial Tree
- Tracking Error and Tracking Risk
- Continuous Uniform Distribution
- Normal Distribution
- Univariate Vs. Multivariate Distribution
- Confidence Intervals for a Normal Distribution
- Standard Normal Distribution
- Calculating Probabilities Using Standard Normal Distribution
- Shortfall Risk
- Safety-first Ratio
- Lognormal Distribution and Stock Prices
- Discretely Compounded Rate of Return
- Continuously Compounded Rate of Return
- Option Pricing Using Monte Carlo Simulation
- Historical Simulation Vs Monte Carlo Simulation

# Safety-first Ratio

Roy’s Safety first criterion states that the optimal portfolio minimizes the probability that portfolio return, RP, falls below RL.

According to this criteria, we select the portfolio with the highest safety first ratio (SFRatio).

**Example**

An investor has a minimum threshold of 2%. He has to make a choice between two portfolios A and B.

| Portfolio A | Portfolio B |

E(R) | 10% | 15% |

s | 20% | 25% |

According to Roy’s Safety-first criteria, which portfolio should he choose?

SFRatio of Portfolio A = (10-2)/20 = 0.40

SFRatio of Portfolio B = (15-2)/25 = 0.52

According to safety-first criteria, we should select portfolio B. Minimum threshold is 0.40 standard deviations away for portfolio A while it is 0.52 standard deviations away for portfolio B.