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Alpha Theory Blog - News and Insights

June 04, 2018

Don’t Double Discount your Discounted Cash Flow


I was working with a client recently and we were discussing their use of discounted cash flow analysis (DCF). Most of our clients are value investors, so DCF is a key tool for many of our clients, especially when valuing businesses where the major value to be unlocked is more than a year in the future.


Here is the problem. The client was double discounting the risk-premium in their discount rate. What exactly does it mean?


Below is a simple DCF, where there is a single stream of cashflows. The investor picks a terminal date and terminal multiple and then discounts the Terminal Value back to today. The discount rate is usually a combination of the risk-free rate and a risk premium (cost of capital) that accounts for the “riskiness” of the stream of cashflows. One of the biggest challenges is the sensitivity of the discount rate. Small changes of large impacts on the total value (there is a 15% difference in valuation if I use 2% above or 2% below the current discount rate).


Screen Shot 2018-06-04 at 11.09.25 AM


The most subjective assumption in the analysis above is the risk-premium in the discount rate. It is required when looking at a single stream of cash flows. But, for investors that use scenario analysis, a risk-premium isn’t required. That’s because the risk premium (the “riskiness” of the cash flow streams) is accounted for in the forecast of risk scenarios with probabilities:


Screen Shot 2018-06-04 at 11.10.12 AM


In this case, only the risk-free rate is needed in the discount rate. The probabilities and multiple scenarios account for the “riskiness” of the cash flow streams.


This benefits scenario-based investors in three ways:

1. NO RISK PREMIUM: The Risk Premium assumption is subjective and creates extreme sensitivity in DCF analysis. Removing this step reduces the noise in the analysis.

2. NO DOUBLE COUNTING: Using this approach means that there is no double counting of risk (risk premium + Risk scenario).

3. EFFECTIVELY ACCOUNT FOR RISK SCENARIOS: What’s the right risk premium to add into the discount rate for a Risk scenario that is bankruptcy. 12%? 18%? 26%? It’s a question that’s not required to be answered when there is an actual probability weighted scenario that includes bankruptcy as part of the entire analysis (now how you size a position by scenario is a topic for another blog).


I think there is general confusion about using DCFs and scenario analysis. For most, DCFs came first. We learned to build them with a single stream of cash flows that were discounted back to present value. We learned scenario analysis at a different time and merged them together on our own. There is overlap in those two methods and hopefully this article will prompt a discussion for those funds using both DCF and scenario analysis.


May 03, 2018

Positive Skew…Part 2 – Maybe It’s Not So Bad for Active Managers After All

In my last post, I discussed the negative impact of positive skew for active managers. Basically, that more than 50% of all stocks in a given market underperform the average because there are stocks that go up more than 100% but no stocks that go down more than 100%. This means that if you pick a random portfolio of stocks from the market, you have a greater than 50% chance of underperforming the market because most portfolios will not hold those few stocks that went up more than 100%.


Because of the popularity of the last post and TV appearance, we spent time digging further into the data to answer questions posed by readers and viewers. We noticed that there was a tendency for the returns between the average stock return and the index return to be different.


And that is the problem with using the average stock return as the hurdle for funds. Investors are not measured against the average stock return, they’re measured against the benchmark, typically the S&P 500. Most indexes are market cap weighted, meaning that the index return and the average stock return are generally different.


In the example below, we’ve taken the current S&P 500 constituents and calculated their return since the beginning of 2012 and compared that to an average return (Equal Weighted) and the actual return of the S&P 500. The S&P 500 over that period was up 136% vs 175% for the average stock (this isn’t a perfect analysis because the constituents in the portfolio changed over that time but it is an approximation).


Positive Skew-part2


The graph above shows the distribution of individual stock returns over that period. You can see the outliers that pull the average stock return (red line) up to a point where 63% of individual securities underperform the average of 176%. But the S&P 500 was up 136% (green line) over that period so only 51% of stocks underperformed the benchmark. Pretty much a coin flip.


We brought positive skew up with Andrew Wellington at Lyrical Asset Management. They have done some great analysis comparing the top 1000 stocks by market cap in the US to the S&P 500 each year going back to 1998.



Source: FactSet and Lyrical Asset Management


As you can see in the chart above, the average stock beating the S&P 500 index is a coin flip. For the past 20 years, the likelihood of any individual stock beating the S&P 500 in any given year is 50.2%. If I build random portfolios using the Top 1000 stocks in the US, there is a high likelihood that the portfolio return will be close to the S&P 500 return.


Some years are clearly better than others. ’98 and ’99 were horrible stock picking years. If you didn’t own the few stocks that had meteoric rises, you had a high likelihood of underperforming the S&P 500. ’01 and ’02 were good stock picking years. Over 60% of stocks beat the index.


What this means, is that any given fund’s batting average should be compared to the batting average of the universe of stocks compared to the benchmark. A 54% batting average in ’98 is heroic, in ’03, 54% is just inline. Take a look at 2017. It was the 3rd hardest stock picking environment in the last 20 years using this metric.


But what about other indices? Thankfully, our friend Julien Messias from Quantology Capital Management has done the analysis (1999-2014) comparing the S&P 500 and Russell 2000. Below are thoughts from Julien on the topic:


The Russell 2000 components returns exhibit a much more leptokurtic distribution (fat-tailed) than S&P 500, meaning that you have a huge part of the index’s components suffering from huge loss (or even bankruptcies), with an average of more than 60% of the components underperforming the index performance and 2% of the components with huge performance (more than 500% per year). The performance of the index is therefore pulled up by those latter 2%.

Assuming a stock-picker operates at random to choose its investment within the index universe, this means that his performance should be closer to the median performance of the components, than to the index performance itself. Therefore, given that the median performance is almost always lower than the index performance (see chart below), an investor in Russell 2000 securities is very likely to underperform and very unlikely to outperform.

The S&P 500 distribution is much more mean-centered, with very shallow/thin tails, meaning that the average stock picker is much more likely to generate a performance close to the index performance (graph from Lyrical AM) and less likely to underperform.



Source: Quantology CM


The Russell 2000 index more apparently displays the impacts of positive skew because it is less impacted by a contribution of a few very large companies. AAPL, MSFT, GOOG, AMZN make up 12.2% of the S&P 500 while the Russell 2000’s top 4 positions make up 1.7% of the index. The result is that the average of all stocks in the Russell 2000 is much closer to the Russell 2000 index return than the average of all stocks in the S&P 500 (recall the large difference from the 2012 to 2018 analysis that showed the S&P 500 return was 136% vs 175% average of all stocks).


This means that the index chosen as the benchmark for your fund has a profound impact on your ability to beat it. More specifically, the probability of beating the S&P 500 with a random portfolio is 50%, for the Russell 2000, it’s 42%.


There has been quite a bit of press regarding positive skew. It’s a great conversation but, for the average fund that is measured against the S&P 500, the impact is overblown. Almost every investor is compared against a benchmark. I recommend that you dig a layer into your benchmark and measure its positive skew, the likelihood of beating the average stock return, the likelihood of beating the index return, and compare your hit rate against the hit rate each year to know how difficult or easy it was for you on any given year.


Quantology Capital Management Russell 2000 and S&P 500 Analysis:

 ­ Screen Shot 2018-05-03 at 10.03.58 AM Screen Shot 2018-05-03 at 10.05.52 AM

Does not include management fees

Data is cleaned from index turnover, with updates every year