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Handling Negative Valuation Ratios in Equity Portfolio Weights

Article Quant Q&A · Author: ArturoP
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Summary

The document discusses the difficulty of turning an inverse valuation ratio into portfolio weights when its inputs can be negative or near zero. One proposed approach is to maximize EBIT divided by enterprise value instead of minimizing enterprise value divided by EBIT, avoiding one division-by-zero issue. For loss-making companies, another answer suggests defining a separate utility rule, using a different function when EBIT is negative, and making weights proportional to that utility.

Other replies offer distinct approaches rather than a single agreed method: assigning a rare negative enterprise-value company the policy maximum, or solving for positive weights that sum to the portfolio total while making the weighted average valuation ratio neutral. These suggestions are exploratory. They do not establish that negative enterprise value is necessarily attractive, specify how weights should be normalized in every case, or address constraints such as risk, liquidity, and estimation error. The choice of utility and portfolio rules needs investment-policy justification.

Key ideas

  • Replacing EV/EBIT with EBIT/EV changes the objective and can avoid division by zero in the original ratio.
  • A piecewise utility can treat profitable and loss-making companies differently.
  • One suggestion is to cap weights in rare negative enterprise-value cases according to portfolio policy.
  • Portfolio weights can also be framed as constrained positive allocations with a target weighted-average ratio.

Tags

EquitiesFactor investingPortfolio constructionPosition sizing
Full text
# How to work out weights for a portfolio based on an inverse ratio with positive and negative values?


# How to work out weights for a portfolio based on an inverse ratio with positive and negative values?












I am trying to work out how to determine weights for the assets in order to form a portfolio. The ratio I am using is EV/EBIT, hence the smaller the better. The problem is I don't know how to handle it when EV < 0. Obviously that is kind of a 'free lunch' mathematically speaking and I realise the discontinuity at x/0 is what messes things up in a way. Would anyone be able to suggest something?

Thanks!

## Answer by DBS (score 1)

https://quant.stackexchange.com/a/10710

ArturoP, as John said, instead of minimizing EV/EBIT, you could as well maximize the inverse ratio EBIT/EV, thus eliminating the division by 0.

You could think of the ratio (e.g. EBIT/EV) as a utility function, i.e. how well you evaluate a company based on the 2 variables, such as U(EBIT,EV) = EBIT/EV.

You'll notice that the ratio above works well when EBIT >= 0. But it is less intuitive when EBIT < 0, since presumably expansive non-profitable companies are the worst case. A workaround for that could be splitting your domain into 2, and define a negative utility as the example below:

\begin{align*} W \sim U(EBIT,EV) = \begin{cases} \frac{EBIT}{EV}, & \text{ if } EBIT >= 0\\ EBIT.EV, & \text{ if } EBIT < 0 \end{cases} \end{align*}

So that your allocation weights W are somehow proportional to your utility.

## Answer by Tom Au (score 1)

https://quant.stackexchange.com/a/12724

An EV<0 is an "ideal" situation (for a value investor). When you find such a rare bird, give it the maximum portfolio weight allowed by your investment policy.

(Given your statement, "the smaller the better," I'm assuming that your portfolio weights are some "reciprocoal" of your calculated ratio.)

## Answer by arodrisa (score 1)

https://quant.stackexchange.com/a/14792

what I usually do for my calculations is the following. Lets say that we want a neutral EV/EBITDA. And we have our companie's EV/EBITDA: A,B,C. We want to invest 100% and our weights will be called x,y,z.

Therefore we have a system formed with 2 equations and 3 unknown variables: x+y+z=100% A*x+B*y+C*z=0 and 3 constraints: x>0,y>0,z>0.

Just set this on Excel, apply the solver and you will get an easy and fast solution :)

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