# Using cumulative returns to hedge against the overall trend

I am curious about a hypothetical strategy where you are long for a given period (like a year), and at the same time you hedge against the overall trend by going short everyday and accumulating the returns, all this using the same instrument (whether you are using a CALL option or physically having the commodity, etc) Basically compounding all profits. Would this be possible? If so, is there a name for this?

Here's a graph that I did in Matlab. It basically graphs the returns of a stock in a given year vs the compounded daily gains (and shorting those gains to create an inverse graph). The idea originally was basically to create a statistical arbitrage opportunity and obtain a delta neutral position long-term, basically trading variance/volatility.

The red graph is the daily accumulation of returns by shorting everyday for a year, and the blue graph is the appreciation of the stock in a given year. The interesting part of this graph is that for the most part, the difference between the blue graph (holding) and the red one (the compounded daily returns gained by shorting) is mostly positive, so it almost always ends up in a profit. Which sounds strange! it sounds like a perfect hedge, by why isn't anyone talking about this? Am I overlooking something? Do I have a mistake? Is this actually profitable?

Also, here's the code I used to generate the above graph. Please help me out here if you see any mistake!

    DIR = 'D:\hedging firm\';
FILE = strcat(DIR,'AAPL.csv');
KC = asset(FILE);
KC.price = KC.price; %
KC.open = KC.open;
KC.high = KC.high;
KC.low = KC.low;

fees = 0.0035; % Fees in USD per trade

difference_mkt = [];
difference_fund = [];
initial_balance_fund = [];
multiplier = 100;

balance_fund = 0;

n = 252;
k= 0;
for i=k+n+1:length(KC.price)
% SHORT
difference_mkt(i) = (KC.price(i) - KC.price(i-n))/KC.price(i-n)*100;

balance_fund = 0;
initial_balance = 0;
multiplier_mv = 100;
for j=n:-1:0
if balance_fund == 0
balance_fund = multiplier_mv * KC.open(i-j);
initial_balance = balance_fund;
end

multiplier_mv = floor(balance_fund / KC.open(i-j));

daily_gain = (KC.open(i-j) - KC.price(i-j)) * multiplier_mv - fees*multiplier_mv*2;
balance_fund = balance_fund + daily_gain;

end
difference_fund(i) = (balance_fund-initial_balance)/initial_balance * 100;
initial_balance_fund(i) = initial_balance;
end

net_gains = difference_mkt(k+n+1:end) + difference_fund(k+n+1:end);

plot(difference_mkt(k+n+1:end));
hold on;
plot(difference_fund(k+n+1:end));

• What is the difference between being short every day and shorting the stock for a year ? I do not understand your point. If you short the first day, your return is zero and so on for all days, isn't it ? – JeanGuillaume Sep 13 '19 at 8:03
• Do I understand this correctly: you short at each day's open and cover at each day's close, using 'multiplier_mv' to size the position, i.e. the short position size varies every day based on the available capital? – Alex C Sep 13 '19 at 14:29
• @AlexC Yes exactly. I size the position everyday based on the available capital. That's basically the most important thing of this strategy. – Luis Cruz Sep 13 '19 at 16:07
• @JeanGuillaume There's a huge difference as you can see in the graph (the returns are not the same). It's because of volatility and compounding profits. – Luis Cruz Sep 13 '19 at 16:07
• I think I do not understand because, for me, the sum of your short and long position should cancel each other : $P_t(1 + R_t) - P(1 - R_t) = P_t$ – JeanGuillaume Sep 13 '19 at 17:28

If I am reading this correctly, ie you are compounding -1x the daily returns, this is exactly what inverse ETFs do.

The obvious catch is that you have to rebalance your short holdings every day, killing you in transaction costs.

The less obvious, but very significant, risk is that this strategy also invokes "variance drag". Imagine a hypothetical stock that has an equal probability of doubling or halving every day. In the long run, it's expected CAGR will be zero (with a lot of very high and low numbers along the way!). On the short side, the strategy is very unlikely to last the week, because the first doubling event will bust it. This is obviously an extreme example, for purely illustrative purposes. However, the same principle holds in smaller degree to more realistic and less volatile equivalents.

Which is why in your example, Red does OK. Blue falls a lot; Red is short, but only roughly breaks even rather than making equal-and-opposite gains from Blue's declines.

• But what do you mean exactly? Red does way better than blue, specially because you notice how rebalancing daily using the available capital slows down the losses and speeds up the gains thanks to accumulation/compounding. You could even use -2x or even -3x just like many inverse ETFs (as you said), and you would get even better results. I haven't come across of "variance drag" yet, at least not statistically speaking... The probability of winning seems always very high, i.e if you add both graphs, 80% of the times it turns up in profit... almost too good to be true. – Luis Cruz Sep 13 '19 at 16:14
• So blue loses, and red breakeven (optically). But red being short blue, does not make equal-and-opposite gains. Which, I think, is the variance drag. If you reverse the polarity, ie change the sign for blue, so she gains; then I suspect red still loses more than blue gains. I might be wrong, but the mathematics is stacked against red here. I think. – demully Sep 14 '19 at 21:28

Probably you can find some insight here:

The Statistics of Statistical Arbitrage Financial Analysts Journal, Vol. 63, No. 5, 2007

Posted: 2 Oct 2007 Bob Robert Fernholz https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1017307