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Alpha Theory Blog - News and Insights

5 posts categorized "Probability-Weighted Return"

June 1, 2019

Increasing the Probability of Success - Part 2

 

This article is a continuation of Increasing the Probability of Success - Part 1.

 

2. PROBABILITY BUCKETS

In many ways, this is the easiest of all the methods to implement. Predetermine as a firm how many price target scenarios you’re going to forecast per position. For example, let’s say you’re going to do three: Reward, Base, Risk. And for each position, the analyst can choose Low, Medium, or High Probability and you preset the probability distribution. For instance:

 

Screen Shot 2019-05-29 at 9.12.06 AM

 

In this case, probabilities are constrained within a range but allow for some flexibility. What you should expect from your analysts is a normal distribution of probability ranges. Mostly Mediums with a few Lows and Highs. No analyst should have more Highs than anything else. The way to explain this to your team is that Low isn’t bad. It’s just less likely than the average (Medium) name. And vice versa for a High.

 

Probability Buckets are the most common probability recommendation we’ve made for clients. They are a good combination of flexibility and practicability, easy to explain to the team, and an effective audit to determine if analysts are being too aggressive.

 

3. FLEXIBLE PROBABILITIES

 

The book Superforecasting explains how individuals can improve their forecasting skill (if you are a forecasting practitioner you should read the book – see our blog post about it here). One primary trait of Superforecasters is micro-updates. Superforecasters change their probability estimates in small increments with new information. For example, changing their probability of Trump winning the 2016 election from 43% to 45% after getting the latest polling data. These small updates accrue to better forecasting accuracy.

 

Given that fact, you’d think my recommendation would be for Alpha Theory clients to make micro-updates and have lots of flexibility with price targets. My answer is, well, it depends. The incentive for Superforecasters was to maximize their accuracy. The incentive for most analysts is P&L, not accuracy, making them reward seekers. This encourages behavior that increases position size (ie. inflated price targets and probabilities – case in point, the average hit rate for all Alpha Theory clients is 51% however analyst assume they're going to make money 72% of the time).

 

The culture and workflow of the firm determine what makes the most sense. If analysts come up with price targets and probabilities with little to no input from the Portfolio Manager then use Fixed Probabilities and Probability Buckets to reduce the likelihood of them “gaming the system.” If the opposite is true and price targets and probabilities are a collaborative exercise with the Portfolio Manager, then Flexible Probabilities is more than likely ideal.

 

One last suggestion as it relates to setting probabilities: know your funds' historical hit rate. What percentage of positions made money on an absolute basis? And on an alpha basis? What percentage hit their upside price target? What percentage hit their downside price target? Use these to set a baseline for the probabilities of the firm. For example, if the historical batting average of the firm is 51%, then the average probability of hitting the reward target should not be 72%. Keep your probabilities realistic and the portfolio you build will be a more accurate forecast of what you will receive (see the “Probability Inflation” blog post).

 

There is no question that setting probabilities is one of the trickiest parts of scenario-based forecasting. We hope this overview gives you a starting point for how to implement an effective probability setting framework.

 

May 1, 2019

Increasing the Probability of Success - Part 1

 

I was discussing with a new client how analysts should approach probabilities. Probabilities are used in calculating probability-weighted returns by multiplying them by the client’s scenarios of price forecasts to come up with a probability-weighted return.

 

The probability piece is the most subjective part of the probability-weighted return (see our “False Precision” blog post that discusses why it is important to set probabilities), so we came up with several approaches to see what fit best for their firm. I thought I’d share them with anyone that may be struggling with probabilities:

 

1. Fixed Probabilities (Distribution)

Analysts come up with price targets that match the part of the forecast distribution associated with the probabilities. In this example, all positions have a “fixed” 20%/60%/20% probability framework. The goal is to come up with price targets that match those buckets (i.e. what is the 20% risk price target?).

Probability of Success-1

 

This method pulls price targets associated that reflect the probability-weighted outcomes associated with a broad range of outcomes associated with different probability “buckets”. An analyst would iterate the assumptions in their financial model to estimate the extreme outcomes (two 20% probability buckets at the end) and the higher probability outcomes (60% probability bucket in the middle). The result is a price target that blends the possible outcomes in each bucket by their associated probability. Another way to think of this is a cumulative probability distribution.

Normal CDF

 

For example, the analyst may associate-5% sales growth and 10% EBITDA margins as the 20% cumulative probability outcome, 25% sales growth and 40% EBITDA margins as the 80% cumulative probability outcome, and 60% growth and 55% margins as the 99% cumulative probability. There would be many other points in between (represented by the green dots) where the analyst would apply different assumptions in their model.

 

The benefits of this method are that the probabilities are fixed and require no subjective assessment. This method also allows for highly-sensitive models with extreme outcomes to be reflected in the resultant probability-weighted return. The downside of this method is that it is time-intensive and allows no flexibility in the probabilities.

 

April 1, 2019

Why Price Targets are Broken and an Easy Method to Fix Them

 

I used to carefully calculate a price target for every asset I invested in. I was, after all, a sell-side analyst for many years and the price target was a staple. But when I used price targets to actually deploy capital, I was less than satisfied. I always had a nagging feeling that something was missing. It took reading a book on poker theory to wake me up.

 

Great poker players calculate price targets by determining the amount of money in the pot. But they do not stop there. Great poker players determine the probability of winning the pot and combine that with pot size and the amount they have to bet (risk) to determine a probability-weighted return (i.e. if they were to play the exact same hand situation 1,000 times, the return they would expect). Why wouldn’t I do the same thing for every investment I make? Take my price target and combine it with my estimate of downside risk and multiply each times my best guess of the probability of each event occurring.

 

Yes, the probability of winning a hand of poker is different than determining the probability of a stock going from $20 to $40. Poker has aleatory probabilities, which means they are defined by observable statistics and investing has epistemic probabilities meaning that probabilities cannot be determined by historical observation (these are words learned from listening to Ronald Howard, Stanford Business School professor that has studied decision making for the last 40 years). Investors describe the same aleatory and epistemic probabilities with different definitions. Definable probability is called risk, and an indefinable probability is called uncertainty. Uncertainty does not mean we should not use probability, because we are using our “confidence” to influence the investment decision anyway.

 

Gene Gigerenzer describes it like this in his book “Calculated Risk”, “Degrees of belief are subjective probabilities and are the most liberal means to translate uncertainty into a probability. The point here is that investors can translate even one-time events into probabilities provided they satisfy the laws of probability – the exhaustive and exclusive set of alternatives adds up to 100%. Also, investors can frequently update probabilities based on degrees of belief when new, relevant information becomes available.”

 

Many firms have a spreadsheet with price targets for each stock in their portfolio. Their price target represents the value the stock should achieve assuming their thesis is correct. But what if their thesis is wrong? Their price target assumes a 100% probability that their thesis comes true. If that is not the case, then downside risk has to be part of the equation. And if the chance of upside or downside is not a coin-flip, then probability must be assessed. These are the metrics that an analyst should be trying to tease out of their fundamental research because they describe the true expected payoff from the investment. Price target does not give you a probability-weighted return! Anything less than a probability-weighted return requires you to rely on your mental calculator to combine profit, risk, and conviction level.

 

Price Target is the most common measurement used by fundamental money managers to evaluate asset quality. The Price Target represents an analyst’s best estimate of value and is a synthesis of their research. The Price Target is then compared to the assets current price to determine if there is a significant enough dislocation of value to provide the fund an opportunity to profit. The Price Target is dynamic because it can be adjusted as the analyst receives new fundamental data. It can also be used as a trading tool that notifies the fund when to enter and exit positions.

 

For all of its attributes, one inherent flaw has made Price Targets impractical for money managers. Price Target only explains the most likely scenario and thus assumes a 100% probability of its outcome being true. For example, Company ABC is trading at $20 and has just hired a new CEO who is known for cutting costs and improving gross margins. Company ABC has historically had margins and multiples below industry norms. So, in your Price Target, you give the company the benefit of industry margins and multiples and determine the company should be worth $30. This is an implied return of 50% and sounds like a solid story. However, the company is a generation behind in product development, so it may be difficult to generate equivalent margins and the company may have to spend on R&D to catch up with the industry. Additionally, there is an even riskier scenario that the industry continues to outpace Company ABC in product development and their competitive position actually disproves to a point where margins are severely impaired. Maybe these other outcomes are not as likely, but they must be accounted for in the measurement of asset quality.

 

This is where many portfolio managers will assess that the asset has great potential upside to $30 from $20, but there are substantial risks that prevent the fund from taking the exposure that generally would be given to an asset with 50% potential return. In this method, the portfolio manager was forced to use heuristics and mental calculation to adjust for risk. But why force yourself to be a human computer when you have all of the relevant information to make a more accurate decision? The first step is to appreciate that the firm’s thesis does not have a 100% probability of occurring. Once a firm indoctrinates that tenet, it is easy to see that all 50% return assets are not created equal.

 

Let’s use our Company ABC example to fully describe the asset using the analyst’s research. The thesis is that the new CEO will improve margins and the company will receive a multiple in line with the industry. The analyst believes there is a reasonable chance that this occurs, say 50%. The analyst also calculates that if the company was forced to spend more on research and development to catch up from a product standpoint, the stock would be worth $22 and this has a lower chance of occurring, say 30%. Lastly, the chance that the industry advances their lead on Company ABC’s product, severely impacting margins, is about 20% and would probably take the stock down to $10. We have now described the full breadth of our research and we can synthesize it without heuristics or mental calculation:

 

Screen Shot 2019-03-29 at 9.29.58 AM

 

The 18% Probability-Weighted Return (PWR) explains the full breadth of your research, is an accurate measurement to make portfolio decisions and is an apples-to-apples comparison of all assets. But this is just the beginning of the benefits of PWR because assets are now being measured by how much return you gain for a given level of risk.

 

We will continue with our analysis of Company ABC. The analyst is in San Francisco and has just exited a one-on-one with Company ABC’s CEO. He finds out that product development is going ahead of plan at a lower cost and the product should be industry-competitive in the next few months. Let’s evaluate how Price Target and PWR would each deal with this new information. For Price Target, things are going according to plan so we wouldn’t raise our target above $30. With PWR we can confidently assess that our probability of success has increased and our probability of overspending on R&D and falling behind the competition has decreased. We would quickly adjust our assumptions:

 

Screen Shot 2019-03-29 at 9.30.11 AM

 

Using PWR we see exactly how much better our idea is given the new fundamental data and can easily see how much better the position is than it was before. The portfolio manager can be confident in adding to the position and have a sense for how much.

 

The process is so much better using Probability-Weighted Returns. Using Price Targets is certainly better than guessing, but it leaves important information needed to make the right decision. If you’re using Price Targets today, take the time to reassess your approach. Start with downside targets with fixed probabilities (50%/50%) and then, over time, add differentiated probabilities to get the full impact of Probability-Weighted Returns on your portfolio.

 

March 1, 2019

Your Position Size is Wrong: A Plea to Put Down the Mental Calculator

 

Hedge funds throw away half of their potential returns by not explicitly calculating probability-weighted return. After working for a fund and having numerous conversations with hedge and mutual fund managers over the past decade, it is obvious that an overwhelming majority of funds’ mistakes come from poor estimation of risk-reward. In fact, most funds have not explicitly defined an upside price target, downside risk target, and conviction level for each investment in their portfolio. This is because most fund managers trust that they can manage the portfolio in their head. They analyze and discuss the upside, downside, and conviction level for every investment, so they assume these factors’ influence is carefully measured into every decision. But I would posit that there is a distinct difference between factoring in upside, downside, and conviction level through mental calculation and measuring it with probability-weighted return. Why would you trust your mental calculator for such an important decision? Could you imagine a bungee jumper that knows the height of a bridge, tension of the bungee cord, and weight of the jumper but just estimates the correct length of the bungee cord? Absolutely not. For every jump, a calculation is performed to make sure that easily avoidable risk is eliminated. Investors all too often skip the “bungee cord” calculation of probability-weighted return and end up assuming undue risk.

 

Empirical research and common sense prove that probability-weighted return is the optimal method to measure an asset’s quality. But most firms do not use probability-weighted return because it questions the output of their mental calculators. Researchers in Behavioral Finance and Neuroeconomics have cautioned investors for over 30 years that their brain is poorly designed to make financial decisions. Armed with this knowledge, investors still do not adjust their process to eliminate known decision-making frailties. In most cases, these shortcomings can be eliminated by calculating a probability-weighted return for every investment.

 

A quick example from a meeting with a portfolio manager highlights the problem of not using probability-weighted return. I was working with a successful fund manager when I asked for the logic behind the largest position in his fund. He told me that it was a company that he knows well, and he is sure they are going to beat earnings. I asked for his upside target if they beat earnings and the probability of it occurring. His best estimates were a profit of 10% and a probability of 90%. I then asked him to explain what would happen if they did not beat earnings. He described a dire scenario where the stock would be down at least 20% because the Street was expecting a beat. I quickly took his estimates and calculated a probability-weighted return of 7%. This caused the manager to change his exposure to the relatively weak idea. He had all of the correct information in his head, but his mental calculator was being corrupted by his over-confidence in his thesis. If this happened with the largest position in the portfolio, you can guarantee that there are other inefficiently sized positions. 

 

It is all too common that funds perform the intense research to drive the ball 99 yards down the field but do not “punch it in” by explicitly defining upside profit, downside risk, and probability. Probability-weighted return takes into account the full breadth of your fundamental research and creates a discipline that treats each position like it is brand new every day and performance-draining oversight is eliminated. As you can see from the example, calculating probability-weighted return is easy and only requires that the firm explicitly define upside, downside, and probability and then compare the probability-weighted sum to the current price. 

 

Once you calculate a probability-weighted return for every investment in the portfolio, you will quickly point out position sizes that do not match your research. Probability-weighted return becomes the synthesis of your research, the common vernacular of investment discussions, and the anchor for decisions.  Your portfolio generates greater returns because you are continuously improving the portfolio to give more exposure to the firm’s best ideas while constantly pruning the weakest. Return is only half the equation. A portfolio constructed with probability weighted return has considerably less risk. Every decision is now made in the context of downside potential. If the downside risk increases, the probability-weighted return falls, which in turn lowers the position size.

 

The benefits of probability-weighted return position sizing are profound and because the process is based on common-sense and sound math, it will become the de facto standard in the coming years. Some of the brightest fundamental managers in the world have been utilizing this discipline for years and your firm can capture the benefits of probability-weighted return in as little as a few weeks. Make a commitment to put down the mental calculator and you are guaranteed to make better decisions.

 

February 8, 2019

Alpha Theory 2018 Year in Review

 

THE STREAK CONTINUES!  For the seventh consecutive year, Alpha Theory clients have outperformed their peers, more than doubling the returns of the industry average over the same period. This year, our clients beat the primary Equity Hedge index by 3.9% despite missing out on 0.9% of return if they more closely followed the model they built in Alpha Theory. 

 

Screen Shot 2019-02-06 at 12.32.26 PM

 

From a global perspective, Alpha Theory clients and optimal sizing outperformed major indices.

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Despite the difficult year for equity funds, including our clients, who averaged a decline of 3.0%, they still outperformed their peers who experienced an average decline of 6.9%.

Screen Shot 2019-02-06 at 12.35.01 PM

 

Clients would have done even better if they would have more closely followed the model they built in Alpha Theory.

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It was a particularly satisfying year to post these results. The streak of momentum fueled markets transitioned into one with much higher volatility in 2018 and it was great to see that our tool is effective at driving alpha in both types of market conditions.    

 

2018 INDUSTRY TRENDS

Some new trends have started to gain traction across the industry in 2018.  While some larger funds have been headed in this direction for years, the change we saw in 2018 was more widespread adoption—even in smaller funds.  As we talked to hundreds of prospective clients and allocators in 2018, we noticed three major trends in how the most successful PMs are changing their investment strategies:

    1. Leveraging more alternative data sources in their research.

    2. Acute focus on repeatable processes around research, risk, and position sizing.

    3. Emphasis on capturing data that can leverage statistical analysis and machine learning.

 

At first, these three trends seemed unrelated. It was only recently that we realized that they are deeply connected by one dominant trend: the reduction in available alpha due to the ubiquity of research data, increased number of analysts, decreased number of publicly available securities, and the rapid rise in computers ability to find market inefficiencies faster than humans. This is making it virtually impossible to gain a sustainable edge through traditional “stock picking.” Put simply-- the largest traditional source of alpha has almost completely dried up.

 

We are seeing this trend in our batting average data as the average of our clients converges towards 50%. The good news is that there is still alpha out there to be harvested and our data bears that out.  Supporting point 2 above, as you will see in the tables below—our most process-driven clients (as represented by our most active clients based on usage) strongly outperform our most passive users.  We also have several clients who are making deep dives into their historical forecasting data to determine which of their analysts have the forecasting best track records and teasing out the strengths and weaknesses of the poor performers so they can target specific areas of improvement. 

 

Our clients are a self-selecting cohort who believe in process and discipline; process orientation goes together with Alpha Theory software that serves as a disciplining mechanism to align best risk/reward ideas with rankings in the portfolio. Shown below, the most active users as measured by frequency of update, research coverage, and correlation with the model have the highest ROIC.

Screen Shot 2019-02-06 at 12.39.42 PM

 

PROCESS ENHANCES PERFORMANCE

Alpha Theory clients use a process to reduce the impacts from emotion and guesswork as they make position sizing decisions. Alpha Theory highlights when good ideas coincide with largest position sizes in the portfolio. This rules engine codifies a discipline that:

    1. Centralizes price targets and archives them in a database

    2. Provides notifications of price target updates and anomalies

    3. Calculates probability-weighted returns (PWR) for assets and the portfolio as a whole.

    4. Enhances returns

    5. Mitigates portfolio risk 

    6. Saves time

    7. Adds precision and rigor to the sizing process

    8. Enables real-time incorporation of the market and individual asset moves into sizing decisions.

 

DISCIPLINED USAGE REDUCES RESEARCH SLIPPAGE

Alpha Theory’s research not only suggests that adoption of the application by itself leads to improved performance, but actual usage intensity further enhances results.

Usage intensity is determined by:

    1. Percent of Positions with Research

    2. Correlation with Optimal Position Size

    3. Login Frequency

 

OPTIMAL POSITION SIZING REDUCES RESEARCH SLIPPAGE

Comparing clients’ actual versus optimal returns shows:

 

HIGHER TOTAL RETURNS
ROIC is 4% higher.

 

IMPROVED BATTING AVERAGE
Batting Average is 9% higher. Explanation: many of the assets that don’t have price targets or have negative PWRs are held by the fund but recommended as 0% positions by Alpha Theory. Those positions underperform and allow Alpha Theory’s batting average to prevail.

Screen Shot 2019-02-06 at 12.41.17 PM

1. Measured as the average full-year return for clients where full-year data was available, adjusted for differences in exposure, net of trading costs

2. Before trading costs

 

PRICE TARGETS REDUCES RESEARCH SLIPPAGE

Alpha Theory has further found that ROIC for assets with price targets is 4.8% higher than for those without price targets. Some investors chafe at price targets because they smack of “false precision.” These investors are missing the point because the key to price targets is not their absolute validity but their explicit nature which allows for objective conversation of the assumptions that went into them.  Said another way, the requirements of calculating a price target and the questions that targets foster are central to any good process.

Screen Shot 2019-02-06 at 3.46.32 PM

 

Finding alpha will not become easier. It is imperative that the funds of the 21st century develop plans to evolve into new realities. Data and process are critical to that evolution. Let Alpha Theory help you and your team grow to meet the challenges of tomorrow.