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Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference.
The ratio is calculated as =, where is the asset or portfolio average realized return, is the target or required rate of return for the investment strategy under consideration (originally called the minimum acceptable return MAR), and is the target semi-deviation (the square root of target semi-variance), termed downside deviation.
Downside risk (DR) is measured by target semi-deviation (the square root of target semivariance) and is termed downside deviation. It is expressed in percentages and therefore allows for rankings in the same way as standard deviation. An intuitive way to view downside risk is the annualized standard deviation of returns below the target.
Roy's ratio is also related to the Sortino ratio, which also uses MAR in the numerator, but uses a different standard deviation (semi/downside deviation) in the denominator. In 1966, William F. Sharpe developed what is now known as the Sharpe ratio. [1]
Cons • Potentially higher returns than money market accounts • Low $500 minimum deposit (although some funds require $3,000) • Some funds earn tax-free interest • No limits on withdrawals
The comparison of upside to downside risk is necessary because “modern portfolio theory measures risk in terms of standard deviation of asset returns, which treats both positive and negative deviations from expected returns as risk.” [1] In other words, regular beta measures both upside and downside risk.
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