Backtesting portfolio asset allocation

Hello,

I have 4 portfolio strategies I want to backtest. The portfolio strategies come from other 2 codes I created (mean-variance and mean-ES portfolio optimization frontier). Each of these strategies are basically just the weights of five different asset classes in the portfolio(s).

I want to compare the profitability of these four strategies for the period Jan 1st 2000 to May 1st 2014 evaluating the market value of the portfolios at every 10-day interval starting from Jan 1st 2000. All this assuming that I invest 1 million USD in every portfolio and hold the portfolio for the whole period mentioned.

My question is: How can I do this?

Thanks.

Answer 1

[Roger Wohlwend]

Assume that each column in the matrix Prices contains the time series of one your asset classes. Then calculate first the returns of the asset classes.

Returns = diff(log(Prices))

Now calculate the historical portfolio returns.

PortfolioReturns = Returns * PortfolioWeights;

Now let's see what happens to your million dollars:

Portfolio = 1e6 * [1; exp(cumsum(PortfolioReturns))]

Repeat this calculation for every portfolio.

[civs]

Hi Roger,

Thank you for your answer. I actually have the matrix of returns already. It is a 3740 x 5 matrix with every column (from 2 to 6) representing the returns of an asset class. The first column (1) has the dates.

But how do I make sure that I get the market value of every portfolio strategy every 10 days? I am assuming the investor bought these portfolios and held them until the end of the period, and there were no withdrawals during the period.

[Roger Wohlwend]

Assuming you have daily data, just take every tenth data point.