### What’s Up with Up/Down Ratio?

I had a couple of meetings yesterday and in each of them, the concept of Up/Down Ratio (Risk/Reward) popped up. Both portfolio managers calculated the ratio by taking the amount of potential upside for an investment and dividing it by their potential downside. For instance, let's say they were considering an investment in IBM. They would do research on IBM and determine their upside was 30% if they sold a few extra Watsons and would be down 10% if they didn't. The ratio is straightforward, 30%/10% or 3x. The portfolio managers in both meetings said they were looking for Up/Down of 2x or greater and would size positions accordingly to the size of the Up/Down. Sound familiar? Yes, it does sound like Alpha Theory.

Now let me start by saying that by calculating an Up/Down Ratio, these firms are asking important questions about risk and reward and giving the portfolio manager a powerful tool to more efficiently size positions. I can promise most firms are not this disciplined. But Up/Down is so close to great but suffers from two fundamental flaws: 1) Up/Down has scale issues and 2) it gives equal probability of risk and reward. To explain the scale issues, let's compare two other companies to IBM's 3x using the same measure. Homerun Company has an upside of 90% if their new drug is approved and down 30% if it isn't – Up/Down Ratio = 3x. On the other hand, Dull Company, is worth 9% more if it gets a new contract and 3% less if it doesn't – Up/Down Ratio = 3x. All three companies have an Up/Down Ratio of 3x but they're not created equal and they'll affect the portfolio differently. If we assume the upside has the same probability (50%) as downside (50%) then Homerun, IBM, and Dull have expected returns of 30%, 10%, and 1.5% respectively. That's not even close to being equal.

So if managers wanted to make a huge improvement on their Up/Down Ratios, they could just assume equal probabilities of Up and Down and calculate an expected return like I did. 30%, 10%, and 1.5% is more predictive and differentiating than 3x, 3x, and 3x. But they can do even more. By assuming 50/50 for Upside and Downside, they run into the next problem of Up/Down Ratios. Analysts have greater confidence in some bets than they do in others. That difference in confidence should be expressed in how positions are sized. For instance, if the analyst has high confidence in Dull Co., medium confidence in IBM, and low confidence in Homerun Co. we could express that conviction as 90/10, 70/30, and 50/50. This would change our expected returns to 7.8% (Dull Co.), 18% (IBM), and 30% (Homerun Co.) These are the measures that should be used to size positions because they express the research and conviction level while measuring the assets' expected impact on the portfolio (i.e. if I were to invest in each of these assets 100 times I would actually expect to get returns similar to the calculation).

With very little change these firms that are using Up/Down Ratios can convert to an expected return. At a minimum, firms with Up/Down can multiply their Up and Down by 50% to get over the scaling issue. Ideally, firms can take it to the next level by using probabilities to factor in conviction level.