The Gain-to-Pain Ratio

I would like to review a metric that I use  to measure risk management effectiveness.   It is called the Gain to Pain Ratio (GPR).   It is a measurement that helps to measure our returns against the risk we take to obtain those returns.

The GPR ratio expresses the returns in relation of the risk taken by the portfolio.  GPR is the primary performance metric used in Jack Schwager’s book “Hedge Fund Market Wizards”.  The GPR represents the sum of all monthly returns divided by the absolute value of the sum of all monthly losses.   A GPR value above 1.5 is considered to be excellent; a GPR value of 1 is considered to be good, and GPR value of less than 0 is considered to be bad.

Most people use the Sharpe Ratio to measure risks.  The Sharpe Ratio expresses how much excess return you receive for the extra volatility that you endure for holding the riskier asset.

We prefer using the GPR instead of Sharpe ratio because in the Sharpe ratio you get penalized for upside volatility.   We don’t really care to be penalized to the upside; if the portfolio has positive returns we are making money and should not be penalized.

To make the point, let’s review three portfolios that had approximately the same results in a six month period:

Return % Mo. 1 Mo. 2 Mo. 3 Mo. 4 Mo. 5 Mo. 6 Total

Sharpe Ratio

GPR
Portfolio A

0

9.5

(1)

1

(1)

(0.5)

8

0.33

3.20

 

 

 

 

Portfolio B

(5)

(18)

20

1

11

(1)

8

0.10

0.33

 

 

 

 

Portfolio C

6

(3)

4

(1)

4

(2)

8

0.35

1.33

All three portfolios, A thru C, made an arithmetic total of 8% in a period of six months, but the way they arrived to the 8% was very different.  Some were more volatile than others.

Ranking the portfolios by Sharpe ratios from best to worst (higher number to lower number) the raking would be C, A and B.   If we ranked them by GPR the order would be A, C and B.  Both ranking systems agree that portfolio C is the least desirable way to achieve the 8% return.  However, they do not agree on the most desirable.

Notice that in the ranking by Sharpe ratios portfolio C is ranked ahead of A, while by GPR portfolio A is ranked ahead of C.   This is because the Sharpe ratio penalized portfolio A for the large spike to the upside in month 2.  Notice that in portfolio A the largest monthly loss was (1%) while in C the largest was (3%).   Also the sum of all the monthly losses in A was (2.5%) vs. the losses in C was (6%).   As an investor, won’t you prefer the returns of portfolio A instead of C?  I think that having smaller losses is more desirable.  This is why we prefer using GPR as a measure to risk-adjust returns instead of the Sharpe Ratios.

Please note: I reserve the right to delete comments that are offensive or off-topic.

  • Sascha Krüger

    1) “Both ranking systems agree that portfolio C is the least desirable way to achieve the 8% return.”
    –> You mean B.

    2) Regarding the chosen time horizen I would prefer portfolio C because I can see that there ia a positive delta (negative to positive returns) every two months.But in portfolio A just month two was remarkable so I couldn’t differentiate between a lucky punsh and a Joe DiMaggio.

  • kimran

    “GPR value of less than 0 is considered to be bad” <- how can GPR go below 0?