Download N: number of months

Standard deviation
Upside/ Downside capture
dard deviation
An Upside Capture Ratio greater than 100%
indicates that the fund has generally returned more
than the index during periods of positive returns for
the index. A Downside Capture Ratio less than
100% indicates that the fund lost less than the index
during months the index had a negative return. A
negative Downside Capture Ratio indicates that the
fund generally has a positive return in months that
the index has had a negative return.
Standard deviation measures the dispersion of a
data set from its mean. The further the data points
are from the mean, the higher the deviation within
the data set. Calculating standard deviation
involves taking the square root of variance by
determining quadratic variation between each data
point relative to the mean.
In finance, annualized standard deviation is applied
to an investment’s rate of return to measure its
historical volatility.
1
𝜎=√
∑(𝑅𝑗 − 𝜇)2 𝑋 √12
𝑛−1
𝜎: 𝑎𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
n: number of months in the sample
𝑅𝑗 : investment return in month j
𝜇 : average monthly return of the sample
This ratio shows whether a fund has gained more or
lost less than a broad index during periods of
market strength and weakness, and if so, by how
much.
The Upside Capture Ratio is calculated by taking the
fund’s monthly compounded returns annualized
during months when the index has had a positive
return and dividing it by the index’s monthly
compounded returns annualized. The Downside
Capture Ratio is calculated by taking the fund’s
monthly compounded returns annualized when the
index has had a negative return and dividing by the
index’s monthly compounded returns annualized.
Sharpe ratio
The Sharpe ratio is a widely used method for
calculating risk-adjusted returns. It is calculated by
taking the mean portfolio return, subtracting the
risk-free rate and dividing the result by the standard
deviation of the returns. Generally speaking, a
higher Sharpe ratio is associated with a better riskadjusted return. Caution must be used when
interpreting Sharpe Ratios as the methodology is
not flawless since it can be inaccurate when looking
at assets that do not have a normal distribution of
expected returns or for assets that have ‘fat tails.’
Furthermore, the Sharpe ratio does not distinguish
between upside volatility (positive returns) and
downside volatility (losses).
𝑅𝑝 − 𝑟𝑓
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =
𝑅 −𝑟
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝑝𝜎 𝑓𝜎𝑝
𝑝
Rp: portfolio expected/mean return
rf: risk free rate
σp: portfolio standard deviation
12
𝑈𝑝𝑠𝑖𝑑𝑒 𝐶𝑎𝑝𝑡𝑢𝑟𝑒 𝑅𝑎𝑡𝑖𝑜 =
𝑁
⌊∏𝑗,𝑅𝑗𝑚≥0(1 + 𝑅𝑗 )⌋ − 1
⌊∏
(1 +
𝑗,𝑅𝑗𝑚 ≥0
⌊∏
𝐷𝑜𝑤𝑛𝑠𝑖𝑑𝑒 𝐶𝑎𝑝𝑡𝑢𝑟𝑒 𝑅𝑎𝑡𝑖𝑜 =
12
𝑚 𝑁
𝑅𝑗 )⌋
(1 + 𝑅𝑗 )⌋
𝑗,𝑅𝑗𝑚 ≤0
−1
12
𝑁
12
𝑁
⌊∏𝑗,𝑅𝑗𝑚 ≤0(1 + 𝑅𝑗𝑚 )⌋
−1
−1
𝑅𝑗 : 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑒𝑡𝑢𝑟𝑛 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑗
𝑅𝑗𝑚 ∶ 𝑖𝑛𝑑𝑒𝑥 𝑟𝑒𝑡𝑢𝑟𝑛 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑗
N: number of months
Sortino Ratio
Correlation
dard deviation
The Sortino ratio is a variation of the Sharpe ratio
that is concerned with downside volatility as
opposed to general volatility which includes
positive returns. The Sortino ratio takes the fund’s
return and subtracts the minimal acceptable return
(zero percent for the Algonquin Debt Strategies
Fund LP) and divides the result by the downside
deviation. Generally speaking, the higher the
Sortino ratio the better the risk-adjusted return.
𝑆𝑜𝑟𝑡𝑖𝑛𝑜 𝑟𝑎𝑡𝑖𝑜 =
𝑅𝑝 − 𝑟𝑓
𝜎
Rp: portfolio expected/mean return
rf: risk free rate
σ: downside deviation standard deviation
Correlation is a statistic that measures the degree to
which two assets move in relation to each other.
Correlation is expressed by computing the
correlation coefficient which has a value that falls
between -1 and 1. If the correlation coefficient is 1,
then the assets are perfectly positively correlated.
This means the two assets always move in the same
direction. If the correlation coefficient is -1, the two
assets always move in different directions.
𝑟𝑋,𝑌 =
𝐶𝑜𝑣(𝑋,𝑌)
𝜎𝑋 𝜎𝑌
𝑁
1
𝐶𝑜𝑣(𝑋, 𝑌) =
∑(𝑥𝑖 − 𝑥̅ ) (𝑦𝑖 − 𝑦̅)
𝑁
𝑖=1
σ: standard deviation
N: number of observations