Roy's Safety First
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[edit] Roy's Safety-First Criterion
Roy's safety first criterion is a risk management technique that allows you to select one portfolio over another based on the criteria that the probability of the return of the portfolios falling below a minimum desired threshold is minimized.
In other words, say you have two available investment strategies - portfolio A and portfolio B. Your threshold level return (the minimum return that you are willing to tolerate) is -1%. You would want to pick up the portfolio that would provide you the maximum probability of the net return being higher than (or equal to) -1%.
Thus, Roy's safety criterion can be summarized symbolically as:
minimize P(Ra < Rm); where P = Probabily of Ra (The actual return) being less than Rm (The minimum desired return).
[edit] Normally distributed Return
If the portfolios under consideration have normally distributed (see Normal Distribution) returns, Roy's safety-first criterion can be reduced to:
maximize the SFRatio (Safety-First Ration).
Where
SFRatio is defined as [E(Ra) - Rm]/(StdDev of portfolio return)
Where E(Ra) = Expected Return of the portfolio (or the mean of the return),
Rm = Minimum desired return
...
[edit] Example
Thus if Portfolio A has a mean return of 10% and standard deviation of 15%, while portfolio B has a mean return of 8% and a standard deviation of 5%, and we are willing to invest in a portfolio that minimizes the probability of a 0% return;
SFRatio(A) = [10-0]/15 = .67, SFRatio(B) = [8-0]/5 = 1.6
By Roy's Safety-first criterion, we would choose portfolio B as the correct investment opportunity.
[edit] Similarity to Excess Return
SFRatio = (Expected Return - Minimum Return)/(Standard Deviation of Return)
Recall that Sharpe Ratio is defined as excess return per unit of risk, or in other words: Sharpe Ratio = [Expected Return - Risk-Free Return]/(Standard Deviation of Return).
SFRatio has a striking similarity to Sharpe Ratio. Thus for Normally distributed returns, Roy's Safety-first criterion provides the same conclusions (about which portfolio to invest in) as if we were picking the one with the maximum sharpe ratio.
