Roy's Safety-First Ratio-Group No 3-Kaushal Jakhelia

Roy's Safety-First Ratio
An optimal portfolio is one that minimizes the probability that the portfolio's return will fall below a threshold level. In probability notation, if R_P is the return on the portfolio, and R_L is the threshold (the minimum acceptable return), then the portfolio for which P(R_P < R_L) is minimized will be the optimal portfolio according to Roy's safety-first criterion. The safety-first ratio helps compute this level by giving the number of standard deviations between the expected level and the minimum acceptable level, with the higher number considered safer.

Formula 2.32 SFRatio = (E(RP) - RL)/ σP

Where:

R_P =Portfolio Return

R_{L =} Portfolio Level Return

Business Application:

For the next year, the manager of a $120 million college endowment plan has set a minimum acceptable end of year portfolio value of $123.6 million. Three portfolios are being considered which the expected returns and standard deviation have shown in the first two rows of the table. Determine which of these portfolios is the most desirable using Roy’s safety first criterion and probability that the portfolio value will fall short of the target amount.

Portfolio	Portfolio A	Portfolio B	Portfolio C
E(Rp)	9%	11%	6.6%
SD	12%	20%	8.2%

Roy’s first safety criterion:

The Threshold return is R=(123.6-120)/120=0.030=3% The SFR shown in the table below. As indicated the best choice is Portfolio A Because it has largest  SFR.

Portfolio	Portfolio A	Portfolio B	Portfolio C
E(Rp)	9%	11%	6.6%
SD	12%	20%	8.2%
SFR Ratio	0.5=(9-3)/12	0.4=(11-3)/20	0.44=(6.6-3)

Analysis: The Probability of an ending value for probability A less than $123.6 million (a return less than 3%)is a simply F(-0.5)which can find on the z-table for Negative value. The probability is 0.3085=30.85%