Measuring Returns on a Short Portfolio with Negative Value

Summary

The note explains why dividing one negative portfolio value by another can produce a return sign that conflicts with the economic result. Its example starts with a short position that makes the securities value negative, then shows the liability shrinking as the security price falls. Cash from the short sale remains in the account until the position is covered, so securities value alone does not represent total portfolio value.

The account ledger combines cash and securities to track equity through the trade. In the example, the short sale leaves total value unchanged at entry, and the decline in the shorted security increases total portfolio value. The lesson is to measure returns from the full account value, including cash and liabilities. The explanation assumes the negative value comes from a short position; other causes of negative portfolio value may require different treatment.

Key ideas

• A negative securities value can represent a short liability rather than a loss in total account equity.
• Cash proceeds from a short sale remain part of the account until another transaction changes the cash balance.
• Track portfolio returns using total value across cash and securities, rather than interpreting the change in the negative position alone.
• A falling price of a shorted security reduces the liability and increases the portfolio's total value.

Tags

# portfolio returns when portfolio value is negative


# portfolio returns when portfolio value is negative












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?

## Answer by amdopt (score 4, accepted)

https://quant.stackexchange.com/a/38671

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.