**Thoughts on Investing Risk**

In his 2011 letter to shareholders, Warren Buffett offered incisive definitions of investing and risk. Investing is

the transfer to others of purchasing power now with the reasoned expectation of receiving more purchasing power in the future.

Consequently,

The riskiness of an investment is not measured by beta (a Wall Street term encompassing volatility and often used in measuring risk) but rather by the probability — the reasoned probability — of that investment causing its owner a loss of purchasing-power over his contemplated holding period.

Instead of buying a car, investing means funding an entrepreneur who will build a car factory in the belief that the enterprise’s future profits will be worth several cars.

Investing risk is then simply defined as not achieving our goal. It means losing purchasing power. Another wording might be the ‘permanent loss of capital.’ Concretely, risk means ending financially worse off than we started.

**Time horizon**

Buffett then qualifies risk “over [the investor’s] contemplated holding period.” Risk is not objective. It depends on the investor’s objective. It is Monday. You have $100, which you intend to spend on Friday for groceries. Investing that money in stocks on Monday only to sell by Friday to go shopping is extremely risky. Over a week, there is a significant probability of losing purchasing power from stock price fluctuation. Better to hold the funds in a crisp $100 bill.

Extend the timeframe, however, and risk flips entirely. You have $100, which you intend to spend in 20 years. Holding cash means suffering gradual but inexorable erosion of purchasing power through monetary and therefore price inflation. Conversely, over 20 years, stock market returns are almost guaranteed to outpace monetary and price inflation. Better to hold stocks.

A longer time horizon will also impact the stocks to invest in. Long-term investors should look for businesses with favorable tailwinds. They may be offensive advantages such as innovation, or defensive such as competitive moats. As Buffett said

Time is the friend of the wonderful company, the enemy of the mediocre.

**An approach**

Building on Buffett’s insights, we understand that long-term investors should not look to dampen volatility but rather minimize the probability of losing purchasing power over a defined time horizon.

While not claiming this is the only or best approach, here is one.

Instead of discounting ‘riskier’ cash flows at a higher rate, consider a range of outcomes and estimate an expected value. A fair coin paying $1 on head and $0 on tails has a 50c expected value. Instead of discounting $1 harshly, discount 50c as you would other cash flows. This however need not be quantitative. Everything I discuss here can be qualitative or heuristic. The goal is merely to find positive outcomes that compensate for negative ones. If we find investments we believe have positive expected values, we are off to a great start.

That’s because, through the magic of diversification, uncorrelated bets will in the aggregate tend towards the expected value. Flip 100 coins simultaneously and roughly half will land on heads. We should therefore assemble portfolios with a variety of fundamental exposures, or underlying bets. If instead of 30 companies, fund performance is substantially driven by a handful of trends, risk will be higher than hoped. From the bottom up, seek variety in industry, business model, and risk profiles. From the top down, identify trends that could cause several investments to underperform simultaneously.

However, even an uncorrelated collection of positive expected value bets can lead to bankruptcy if we bet too aggressively. This is where the Kelly Criterion comes in. Sizing is a key component of risk management. Better to budget than to discount. Conveniently, Kelly’s definition of risk maps neatly to Buffett’s. Kelly uses upside, downside, and probability of upside as inputs. Risk is the probability of loss multiplied by its magnitude. A company is risky if the downside is bankruptcy, and the likelihood is high. Kelly lets us safely invest in risky companies by keeping their share of the bankroll appropriate. We increase the size proportionally with the expected value and decrease it exponentially with the range of potential future outcomes.

**Conclusion**

Long-term investors should not focus on dampening volatility or discounting risky cash flows harshly. Risk means losing purchasing power. We guard against such outcomes by investing in a collection of uncorrelated positive expected value bets and sizing them appropriately.

*Sacha Meyers*