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Safety-first ratio (安全第一比率):
the distance from the mean return to the shortfall level in units of standard deviation。平均收益与最低可接受的临界收益的距离有多少个标准差。这个比率越大越好,表明单位风险上的收益较高。
注:Safety-first ratio 与sharpe ratio比较相似,中是无风险收益率,而SFRatio中是最低可接受的临界收益。
Shortfall risk (亏空风险):
the risk that portfolio value or return will fall below the minimum acceptable level (RL, shortfall level, threshold level) over some time horizon.
亏空风险是指在整个投资期限内,组合的收益低于最小可接受的回报范围。
Safety-first ratio与Shortfall risk的关系:
Minimizing shortfall risk = Maximizing safety-first ratio
最小的亏空风险等于最大的安全第一比率
例:At the end of the current year, an investor wants to make a donation of $20,000 to university but does not want the year-end market value of her portfolio to fall below $500,000. If the shortfall level is equal to the risk-free rate of return and returns from all portfolios considered are normally distributed, will be portfolio that minimizes the probability of failing to achieve the investor's objective most likely have the:
highest safety-first ratio? highest Sharpe ratio?
A. No Yes
B. No No