Daily Inverse Returns, Rebalancing Costs, and Variance Drag

# Using cumulative returns to hedge against the overall trend


# 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));
```

## Answer by demully (score 2)

https://quant.stackexchange.com/a/48665

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.

## Answer by tdazio (score -4)

https://quant.stackexchange.com/a/48664

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