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The Mathematics of Long/Short

15030169_maths of long short

The Mathematics of Long/Short

Over the past few weeks we have had the pleasure of meeting with clients and friends of the firm around Australia and New Zealand. We are fortunate to have such sophisticated advisers and investors as clients. It makes our discussions detailed and insightful. One subject of interest recently was the performance drivers of, and expectations for, long/short funds. In this article I will put some mathematics and meaning around the topic.


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Christopher is a Portfolio Manager for the Montaka funds and the Montgomery Global funds. He joined MGIM at establishment in 2015.

This post was contributed by a representative of Montgomery Investment Management Pty Limited (AFSL No. 354564). The principal purpose of this post is to provide factual information and not provide financial product advice. Additionally, the information provided is not intended to provide any recommendation or opinion about any financial product. Any commentary and statements of opinion however may contain general advice only that is prepared without taking into account your personal objectives, financial circumstances or needs. Because of this, before acting on any of the information provided, you should always consider its appropriateness in light of your personal objectives, financial circumstances and needs and should consider seeking independent advice from a financial advisor if necessary before making any decisions. This post specifically excludes personal advice.

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  1. Hi Chris,
    A bit too much detail for me :). My main observation is that the market return of 32% is obviously significant better than 20% of the fund. Would you normally expect this level of variation? I invested in the initial offering with a basic understanding that returns could be gained through the long and short side. But for a younger person, without the need to drawdown, then perhaps a long only fund would be the better option.

    • Peter thanks for your interest and your investment. I think it is best to look at the performance of Montaka over its entire life, which is 42.8% through 30 April 2019: https://www.montinvest.com/montaka This compares to 46.2% for world equities (MSCI total return index) both in Australian dollars. So Montaka’s return is almost, but not quite, the same as the market. Return is the observable statistic. The unobservable statistic is risk. Over this period Montaka has generated its near-market return with less than 50% of the fund exposed to the market. So perhaps we could argue that the market associated risk taken by Montaka is half that of an equities fund or the market itself. This doesn’t feel too valuable in a market that has been rising the last few years. But it does provide a substantial amount of capital protection when conditions may not be so favourable (for example, in the last quarter of last year Montaka saved about half of the 11% decline in the market). All the best Chris

  2. Your explanation implies that in a rising market you expect your short portfolio to not only underperform, but to actually lose money. Yeah?

    So in a rising market you would only hold those shorts as a hedge against your long positions?

    I would have expected you could find stocks that go down in virtually all markets.

    Do you expect your short portfolio to generate positive returns over a full market cycle?

    • Thanks for these comments. In a generally rising market it may be hard for some shorts to make money even if they do perform well relatively. There are definitely stocks that can lose money in rising markets. It is impossible to pick the direction of the market especially near term and there is value protecting against adverse market outcomes for many investors. All the best Chris.

  3. Hi Christopher,

    Querie.. If the portfolio was 100% & 0% short using same numbers as you, you get a 13% return.
    If however, market is down 8% then return using your numbers is 2.8% (90% long 50% short) vs 100% long = -3% return.
    Assuming market goes up 60% of the time and down 40% of the time (quite conservative) then return with either portfolio = 6.6%.
    Given the similar returns, the long only portfolio may have more volatilty but the returns are similar to mixed long/short, there is less research required & I assume costs are less.
    So, would it not be better to simply stick with picking best performing stocks only?

    • Joe, thanks for your question. While I see the point you are making there are other moving pieces at play. For instance, volatility and drawdown represent significant risks for some investors (think about retirees in drawdown) and the ability to protect capital during market downturns is valuable in this case. Also the analysis at hand (yours and mine) does not account for the flexibility of the long/short to vary exposure to the market. That is, when stocks and markets are cheaper the long/short can be more net long and vice versa when equities are expensive and risks elevated. This feature of the fund structure can add value. I would also point out that the example I provided used long alpha input (5%) that was better than short alpha input (3%). Changing these around would give a different result, in favour of long/short. So going a bit deeper we can immediately see that it’s not so simple to draw the conclusion that 100% long-only is categorically better than long/short.

  4. Thanks for providing the math’s behind the subject Chris. It has certainly cleared up a few points form me.

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