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I am being very stupid probably but I don't understand the following.

Portfolio 1st Jan valued: -$100

A month later

Portfolio 1st Feb valued: -$45

I calculate the return of the portfolio as,

    ((-45 / -100) - 1) * 100 = -55%

But as I see the value of your portfolio has increased since -45 > - 100 so why is the return negative?

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    $\begingroup$ @muffin1974 apologies I made mistake typing the question. I have -45/-100 - 1 $\endgroup$
    – mHelpMe
    Commented Feb 19, 2018 at 14:47

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Assuming the 'portfolio value' is negative because of a short position, you need to reconcile it vs. the accounts cash position.

For example, below the account sold 100 worth of securities short on Day 1 and that security declined in value by 55% on Day 2--decreasing the portfolio liability. The Cash position does not change until another transaction is made. I have added a Day 3 where the portfolio is completely in cash after the short position is covered as of the Day 2 close of business.

        Cash    Securities  Portfolio Value %Return
Day 0   100     0           100 
Day 1   200     -100        100             0%
Day 2   200     -45         155             55%
Day 3   155     0           155             55%
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