CAIA LEVEL 1 2.5 QUESTIONS AND ANSWERS.

Semi standard deviation Volatility of returns falling below the mean. Also called downside standard deviation Semi variance The square of the semi standard deviation Semi standard deviation Mean I hesapla. Mean den kucuk rakamlari alarak ( r-m)nin karesi +... Cikan rakam /n-1 = sample semi variance , bunun karekoku sample st deviation semistandard deviation = ∑ (Rt −μ)2 /T forRt<μ The difference between semi standard deviation and standard deviation the target semistandard deviation focuses solely on negative surprise outcomes: Rt < TR. In contrast, the standard deviation uses all returns, including both positive and negative surprises. Second, the target semistandard deviation uses a customized reference point, or target return TR. In contrast, the standard deviation uses the historical mean return for the fund. Shortfall risk The probability that the investment return will fall below the target return is called shortfall risk. Target semi standard deviation Measures the volatility of returns falling below a pre specified target. Semi standard deviation equals the volatility of returns falling below the mean. Tracking error Tracking error measures the extent to which the investment returns deviate from the benchmark returns over time. Therefore, tracking error quantifies the uncertainty (risk) regarding deviations of the investment return from the benchmark return. Tracking error A low tracking error indicates that the investment performance closely resembles that of the benchmark. The tracking error is especially useful for a manager with a relative return mandate. Tracking error tracking error = T ∑(Rt −RB −M)2 / T−1 where: RB = benchmark return M = mean difference between the investment return and the benchmark return Drawdown Drawdown equals the percentage decline in asset value from its previous high. In determining the drawdown, the high point is referred to as the peak and the low point is referred to as the trough. For example, assume the fund value recently peaked at 100 and now equals 80 at the trough. The drawdown equals 20%. Drawdowns are more intuitive than volatility risk measures. Maximum drawdown Maximum drawdown is the worst percent loss experienced from peak to trough over a specified period of time. VaR Value at risk (VaR) is a measure of potential loss. VaR is interpreted as the worst possible loss under normal conditions over a specified period for a given confidence level. VaR strength The strengths of VaR are that it is simple to apply, can be applied across segments within a fund or across funds, and is useful when examining the worst-case scenario is unnecessary. VaR weakness A major weakness of VaR is that it can be misleading for non-normal distributions. For example, consider a fund with a 98% probability that its annual profit will equal $50,000, but with a 2% probability that it will lose $1 million. A manager using a 95% VaR will reach a much different conclusion than a manager using a 99% VaR Conditional VaR Conditional VaR (CVaR), also known as expected shortfall expected tail loss, is the expected loss given that the portfolio return already lies below the pre-specified "worst case" quantile return (i.e., below the 5th percentile return). In other words, expected shortfall is the mean loss among the losses falling below the q-quantile. Parametric VaR Parametric VaR is a specific form of VaR that assumes returns are normally distributed. By using the properties associated with the normal distribution, the VaR for a given confidence level can be calculated relatively easily. Calculate the 100-day, 95% parametric VaR in dollars for a $100 million portfolio with a daily standard deviation estimated at 2%. parametric VaR = 1.65×0.02× (square root of 100) ×$100 million = $33 million Parametric VaR calculation In this example, there is a 5% chance that the portfolio's value could fall 33% or more in a 100-day period. This percentage loss is multiplied by the dollar amount of the portfolio to determine the VaR in dollar terms. For this example, the 33% loss on the $100 million dollar portfolio produces a VaR of $33 million. VaR / z values 90% VaR: Use a z-value of 1.28. 95% VaR: Use a z-value of 1.65. 99% VaR: Use a z-value of 2.33. Historical volatility The volatility figure most often used for VaR is historical standard deviation. Other historical volatility methods include the ARCH and GARCH models (discussed in the Statistical Foundations topic review) that estimate volatility by placing greater weight on more recent data than older data. Implied option volatility This volatility approach utilizes the implied volatility derived from option pricing models. If option volatility is accessible, this volatility estimate is usually preferable as it inherently includes expected future drivers of volatility (some of which may not be found in historical data) and can be immediately adjusted for changing market conditions. leptokurtic distribution are "fat tailed" with greater frequency of extreme outcomes VaR should use a distribution that allows for fat tails, such as a mixed distribution or the Student t-distribution. An alternative and simpler solution is to increase the number of standard deviations. For example, for a 95% confidence level, use a number greater than the z-statistic of 1.65. The magnitude of the number depends on the perceived size of the tails of the empirical distribution.