03 Method.html

<p>We first gather 100 points of historical closing prices for BTC, BCH, ETH, and LTC. Using OLS, we regress BTC prices (we label BTC as the <em>anchor</em> in the code) against BCH, ETH, and LTC prices to create the following regression equation:</p>

\[P_{BTC} = \alpha + \beta_{BCH}P_{BCH} + \beta_{ETH}P_{ETH} + \beta_{LTC}P_{LTC}\]

<p>Using this relationship, if we long 1 BTC, we take a position of -<em>&beta;</em>{BCH, ETH, LTC}. Let this scenario be called &ldquo;buying the portfolio&rdquo;. If we go short 1 BTC, we take a position of <em>&beta;</em>{BCH, ETH, LTC}. Let this scenario be called &ldquo;shorting the portfolio&rdquo;.</p>
<p>We then take the residuals of the OLS Regression and test them at the .05 significance level for both the augmented Dickey-Fuller and Phillips-Perron test. These are two different tests for stationarity, which helps us determine if the portfolio has mean-reverting qualities. If either test fails, we stop the trading.</p>
<p>To generate the rules of trading, we first compute the portfolio values of holding 1 BTC and -<em>&beta;</em>{BCH, ETH, LTC}, and from these portfolio values we compute the mean (&mu;) and the standard deviation (&sigma;). Then, if the value of the current portfolio trips below and then above &mu; - 1.5&sigma;, we buy the portfolio, and if the value of the current portfolio trips above and then below &mu; + 1.5&sigma;, we short the portfolio. Please note that the paper buys and sells the portfolio on the initial trips of the levels, however, we noticed that by waiting until the portfolio trips the levels the second time, we significantly reduce the drawdown and the losses.</p>