Omega Ratio by Keating and Shadwick

December 15th, 2013, 04:35 AM

Paper:

https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Keating_An_introduction_to.pdf

Is anyone using the Omega Ratio in their portfolios?

I am looking for measurements that work well with a portfolio with a large number of trades that are not easily influenced by outliers.

Mike

December 15th, 2013, 04:36 AM

R's PerformanceAnalytics package already includes Omega, for those who are using R.

Code

function (R, L = 0, method = c("simple", "interp", "binomial", 
    "blackscholes"), output = c("point", "full"), Rf = 0, ...) 
{
    method = method[1]
    output = output[1]
    if (is.vector(R)) {
        x = na.omit(R)
        switch(method, simple = {
            numerator = exp(-Rf) * mean(pmax(x - L, 0))
            denominator = exp(-Rf) * mean(pmax(L - x, 0))
            omega = numerator/denominator
        }, binomial = {
            warning("binomial method not yet implemented, using interp")
            method = "interp"
        }, blackscholes = {
            warning("blackscholes method not yet implemented, using interp")
            method = "interp"
        }, interp = {
            a = min(x)
            b = max(x)
            xcdf = Hmisc:::Ecdf.default(x, pl = FALSE)
            f <- approxfun(xcdf$x, xcdf$y, method = "linear", 
                ties = "ordered")
            if (output == "full") {
                omega = as.matrix(cumsum(1 - f(xcdf$x))/cumsum(f(xcdf$x)))
                names(omega) = xcdf$x
            } else {
                omegafull = cumsum(1 - f(xcdf$x))/cumsum(f(xcdf$x))
                g <- approxfun(xcdf$x, omegafull, method = "linear", 
                  ties = "ordered")
                omega = g(L)
            }
        })
        result = omega
        return(result)
    }
    else {
        if (length(Rf) > 1) 
            Rf <- mean(Rf)
        if (length(L) > 1) 
            L <- mean(L)
        R = checkData(R, method = "matrix", ... = ...)
        if (output == "full") 
            R = R[, 1, drop = FALSE]
        result = apply(R, 2, Omega, L = L, method = method, output = output, 
            Rf = Rf, ... = ...)
        if (output != "full") {
            dim(result) = c(1, NCOL(R))
            rownames(result) = paste("Omega (L = ", round(L * 
                100, 1), "%)", sep = "")
        }
        colnames(result) = colnames(R)
        return(result)
    }
}

Mike

May 12th, 2019, 10:51 AM

Little bit of forum necromancy here, trying to bring alive a five year old post.

WOW. Simply WOW. I knew about Sharpe and it's problem of also penalizing good volatility and how Sortino attempts to fix that. I know about Sterling and Calmer. But I had never heard of the Omega Ratio. I'm very surprised that this thread got no responses at the time, and that futures.io has no other threads on Omega Ratio. The linked document is super interesting with explanations of the weaknesses of other methods* and how Omega includes higher moments of distributions.

The obvious issue is that other metrics (like Sortino) give you a single number, while Omega is dependent upon your desired rate of return. Portfolio A might be better than B when you want a X% return, but B is better than A when you want Y%. But is it as simple as X and Y? Aren't we generally just looking for the highest return, with the lowest risk?**

* The illustration of the flaws of a Sharpe Optimal Portfolio was excellent but the lack of an explanation of how you would construct and Omega Optimal Portfolio was disappointing!
** Haven't investigated this in anyway, but writing this I just thought maybe a ratio of two different Omega's, say the Omega of a zero return divided by the Omega of -10% return but be interesting

May 12th, 2019, 11:32 AM

SMCJB

** Haven't investigated this in anyway, but writing this I just thought maybe a ratio of two different Omega's, say the Omega of a zero return divided by the Omega of -10% return but be interesting

Wouldn't be a ratio because you want both of the Omega scores to be as high as possible, so maybe sum or product.

July 1st, 2019, 01:43 AM

Hi SMCJB,

I can't insert links, but if you search on "calculate-the-omega-ratio-with-excel" you'll find an article about Omega ratio.

I have found the following description:

The Omega Ratio contains much more information about the return distribution, including the mean, variance, skew and kurtosis and is especially valuable for non-normal investments (such as Hedge funds, options, futures and derivatives).
Several years ago, hedge funds were subject to large losses which were in no small part due reliance on standard mean-variance optimization techniques (as pioneered by Markowitz). These approaches use mean and variance as a proxy for risk. However, this presupposes normally distributed returns; this is not the case for leveraged investments like hedge funds. Since then, the Omega Ratio and other similar approaches have grown in popularity because they favour investments with a lower probability of extreme loss.

The article also has source code as how to calculate Omega in Excel / VB.
I coded it in C++.

===

I have an automatic trading system. Part of the system evaluation are Sharpe ratio, Sortino ratio, Kelly criterium and Omega ratio.

One could calculate Sharpe ratio by hand. IMO for Sortino, Kelly and Omega manual calculations are not practical.

I find Sharpe and Sortio still valuable for a quick estimation of profitability & risk, Kelly is good for position sizing.

I use Omega to establish system profitability in respect to costs (= minimum profitability threshold). I set my minimum required profitability at 100 USD per day. An Omega of 1.0 or larger indicates I expect to cover 100 USD on costs per day. Calculation are including spread and commissions.

Omega Ratio by Keating and Shadwick

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Omega Ratio by Keating and Shadwick