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Alpha Theory Blog - News and Insights

September 29, 2021

The Cost of Volatility – The Path Dependency of Returns


In a recent analysis, we were comparing the volatility of a return stream on a daily and monthly basis. We all know that if a portfolio goes down by 10%, it must be up more than 10% to get back to even (11.11% to be exact). The path dependency can cause the differences in return and volatility to be stark. In trying to understand where the differences arise, we compared the outcomes of a perfectly stable return stream (0% volatility) to those of increasing levels of volatility.


Cost of volatility


The starting point is an ideal 20% return (blue line) over the course of a year (252 days). The most efficient way to create that return is to generate 0.072% of return per day. Any additional volatility, with the same average of 0.072% return, negatively impacts total return. To show the impact, we simulated six return streams that all had an average of 0.072% daily returns but with varying daily volatilities between 0% and 5% (5% daily volatility is 79% annualized volatility).


For example, with 1% daily volatility (orange line), the daily return flips between 1.071% and -0.926% (average of 0.072%). For 5% volatility (green line), the daily returns flip between 5.066% and -4.922% (also a 0.072% average).


Volatility is a cost that requires a higher average return to get to the same goal. Ex-post (after the goal is reached), if you achieve a 20% return from two assets, you do not care about the path (volatility) that led to the 20% return. On the other hand, ex-ante (before the bet is made), it is harder to get to a 20% return with a 5% vol than a 1% vol.


The compounding impact of volatility is difficult to conceptualize but is important to understand when making investment decisions. This graphic is hopefully a helpful tool to remember how volatility causes us to raise the return bar for an asset.


As a life-long fundamental investor, acknowledging volatility as a risk is a tough pill to swallow. In my career as an analyst, I made forecasts over long periods of time, and I did not care about the path, just the outcome. However, before the bet is made, if I have two assets with the same probability-weighted return of 20% and one has a volatility of 10% and the other 30%, should I be indifferent or should I factor that in to how I size my bet? And if so, how? These are interesting questions that we’ll continue to explore in future posts.


August 31, 2021

Caveats in Compounding


“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it.” – Albert Einstein


“Compounding is the most powerful force in the universe” – Albert Einstein


“My wealth has come from a combination of living in America, some lucky genes, and compound interest.” – Warren Buffett


Compounding really is the 8th Wonder of the World. In a recent analysis, we were comparing the CAGR (Compound Annual Growth Rate) of two portfolios and noticed two unique qualities of compounding that are important to remember when using CAGR:


1. Small differences in CAGR can compound to large differences over time

2. A 1% difference in two small CAGRs is not the same as a 1% difference in two large CAGRs


Small differences in CAGR can compound to large differences over time


Imagine you have two portfolios. One generating 8% per year and another 9%. The 1% difference seems trivial. Because of compounding, it is not.


Screen Shot 2021-08-31 at 3.19.42 PM


The 10-year performance difference is a non-trivial 20.8%. This means that finding investments that may seem marginally different when compared at the small scale of a year, can have profound differences over time.


One interesting fact was that the total difference over ten years was 20.8%, which is not the same as the 1% difference compounded over 10 years, which is 10.5%. This leads to the second unique quality…


A 1% difference in two small CAGRs is not the same as a 1% difference in two large CAGRs


If we bump the performance slightly up but keep the difference 1%, the total difference grows from 20.8% to 22.6%.


Screen Shot 2021-08-31 at 3.19.51 PM


That 1% difference gets to compound a bigger base and thus results in a larger total return difference. This is counterintuitive. An investor may be indifferent between a 23% and a 24% return while being sensitive to a 2% versus 3% return. The later seems much more meaningful because the relative difference is 50%.


In the graph below, the difference between a 2% and 3% return is $12.5M (12.5% on $100M fund) over 10 years. The difference between a 23% and 24% return is $62.1M! They are both 1% differences, but they are not created equal.


Screen Shot 2021-08-31 at 3.21.54 PM


Compounding is amazing but can be amazingly difficult to conceptualize. As an investor, your job is to be a professional compounder. Keep your tools sharp by remembering that CAGRs don’t tell the whole story. To get a better sense of the return stream, compare the CAGR to the total return for a period of time and then perform some basic sensitivity analysis. This allows the compounding impact on returns to present itself in a way that is easier to put into perspective and help you make better decisions.