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Say the example market return is 12% for the year, I managed to develop a 3-4 Sharpe strategy that makes 6% a year. If I can borrow twice the size of my original fund at 0% interest, I can make more than the market return while still having less risk.

Theoretically, it can also mean I should borrow as much money as I possibly can, as long as the interest rate is lower than the return of my strategy, and as long as the total risk is less than the overall market risk.

If that is the case, what are any other reasons why I shouldn't borrow up to my (risk, interest) limits?

Edit: I'll try a more extreme example to make things more clear. Say I have a hedging strategy that only nets me 2% per annum, but the maximum drawdown is 0.1%. Assuming I can borrow at 0% interest and the maximum drawdown of the market is 10%, theoretically I can borrow at 100x leverage and get 200% while still sharing the same 10% drawdown as the market.

Realistically, this wouldn't happen because its hard to borrow anything at <2%, but if I really could, what is stopping me from doing just that?

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    $\begingroup$ Nothing, in short. What you present is entirely theoretical however from the calculation you're using to get a '3-4 Sharpe strategy' to borrowing at 0% interest to a 12% market return. On the other hand, if you have a genuine 3-4 Sharpe strategy (ie, no data mining or other bias) that doesn't involve selling tail risk and isn't severely constrained (ie, high frequency) please take my money. $\endgroup$
    – Chris
    Nov 3 '20 at 6:58
  • $\begingroup$ Uncertainty about the Sharpe ratio (and overall performance) going forward. How do you know your strategy has a Sharpe ratio of 4? $\endgroup$
    – fesman
    Nov 3 '20 at 9:24
  • $\begingroup$ I suggest you look at margin requirements for futures (on the exchanges' websites) to get an idea of what leverage is possible. $\endgroup$
    – user42108
    Nov 3 '20 at 14:07
  • $\begingroup$ With the edit to the question, I wonder what maximum drawdown has to do with leverage and borrowing when it is merely a technical indicator of downside risk/peaks/troughs. I hope it's not being conflated or confused with drawdown products which on the other hand are connected to leverage and borrowing $\endgroup$
    – develarist
    Nov 3 '20 at 16:23
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Not sure if "3-4 Sharpe" indicates the value of the Sharpe ratio you're earning since such magnitude is meaningless without some benchmark to compare against, due to it being a purely relative measure. Anyway, we can talk about 6 things that should stop you from using high leverage:

  1. Surprise bear market
  2. Asymmetric tail dependence
  3. Sharpe ratio misestimation
  4. In-sample performance exaggerates ($\neq$) actual performance
  5. Backtesting technique was wrong
  6. Prospect theory (asymmetric investment behavior)

It isn't hard to make positive returns, regardless of strategy, in a year that is providing 12% on the market. Are you confident enough to believe that your same strategy will still make 6% in a bearish economy that is providing -2% per year instead? Or will it triple the loss that the market is losing? Maybe you have thought that you don't stand to lose anything.

There are asymmetries to think about. More specifically, asymmetric tail dependence between asset returns, in that asset returns are likely to fall harder when the bearish regime comes around because of high correlation in the lower-tail-dependence than they were doing in the not-as-correlated upper-tail bullish regime which was the only scenario you backtested your strategy on. All you need to do is get the bull/bear bet wrong and the magnitude of risk-taking becomes less of an important indicator. Only the mere act of having borrowed any amount whatsoever in the first place becomes the regret in hindsight. Nevermind betting wrongly as to the direction of interest rate movements when they finally do turn non-zero. But you can look into bet-sizing if you want.

As a performance measure, the Sharpe ratio itself is flawed because it consists of asset means $\mu$, which is known to suffer from misestimation error. Setting up a strategy based on in-sample data, therefore, is likely to disappoint out-of-sample when statistics diverge from what they were in-sample. Minimizing variance alone, rather than the Sharpe ratio, is automatically more impressionable of a strategy since volatility $\sigma$ is easier to estimate than $\mu$, and therefore has superior out-of-sample performance than allocating based on the Sharpe ratio. If anything, the Sharpe ratio should only be used to evaluate performance after the fact, not to initiate trades.

Stating that you managed to construct a strategy that accomplished some feat should seriously be re-considered over in terms of how you properly you backtested it. Alot of backtests are done wrong leading to disappointment when a poorly-backtested strategy is actually implemented in real life.

As much as you might think that borrowing at 0% is free money, the reality is that you are likely going to be magnifying any losses you make. The more you have to put on the craps table, the more you are putting up to lose, your money or free money. Losing 10% of \$1,000,000 has a larger emotional impact than 10% of $10,000 no matter the source of funds, which is kind of explained by prospect theory in behavioral finance. Believing you are a guru in a bullish market is normal, so gains of any order are treated indifferently and happily accepted, unlike the two different loss scenarios just described, reflecting the asymmetry that the prospect of gains evokes in investment behavior versus loss aversion. Then again, maybe you have thought that you don't stand to lose anything.

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For the very simple reason that risk premium is a premium for a good reason that it may kills you before you get the profit?

Finding the optimal asset allocation to balance the need of money and safety is a substantial academics field, some academics Indeed suggest leverage at young age.

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  • $\begingroup$ All the answers are great but the OP has a point in that leverage is how many well known hedge funds generate high returns. In fact, the SR of the original strategy ( compared to some benchmark ) doesn't have to be so high as long as one is VERY confident that it's +. Also, some hedge funds have long standing credit relationships so the amount that they can leverage is a lot larger than the amount that you can leverage. Leverage is why many hedge funds quickly fire PM's when they are losing money. The amount the PMs are costing the owner is a lot more than it might look to them !!!!! $\endgroup$
    – mark leeds
    Nov 2 '20 at 19:05
  • $\begingroup$ If it is a high Sharpe, the maximum drawdown is less than the market because the standard deviation is lower than the return in a relative context. Say if I use 2x leverage on a 4 Sharpe strategy, I would get 12% (same) return as the market while suffering less drawdown than the market itself. So if market's drawdown is 10%, maybe mine would be 6% after leverage. That means that I could borrow all the way until my maximum possible drawdown (risk) matches the market of 10%, and potentially get my returns more than the original 12%. I had some good answers on why that may not work. $\endgroup$
    – David LE
    Nov 2 '20 at 23:34
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"what are any other reasons why I shouldn't borrow up to my (risk, interest) limits?"

The peso problem.

Nobody is going to lend you money at 0%. Best-case scenario for an institutional investor is PB funding rate + spread, with limits on your leverage depending on the asset class.

EDIT: perhaps should have added that a strategy with a Sharpe of 3-4 is likely to be capacity constrained, meaning that some level of leverage, perhaps relatively low, will begin to eat into the returns via market impact.

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