In graduate school I was spoon fed modern portfolio theory as the best way to construct a portfolio using mean - variance optimization based on historical asset price action. It’s an elegant, brilliant model and before Markowitz we really had no mathematical construct to gauge risk/reward in a portfolio. But over time I have strived to better understand the assumptions that were needed to make the math work. Which has led me to my main question:
If MPT uses average annual (arithmetic) returns for its basis, how does it maximize the long term compounded (geometric) returns we are striving for? Does it have some blind spots?
I have come to the following conclusions:
1) MPT is a single period model using historical data to predict expected (mean) returns for the next period.
2) So MPT doesn’t really address compounded returns over a multi period time frame. Eg. It’s missing the volatility drag component that reconciles arithmetic and geometric returns.
3) therefore, higher volatile investments maybe riskier than predicted by MPT over a multi period time frame.
4) the Kelly Criterion could be a better model for maximizing compounded returns
Personally I use MPT as my portfolio basis for diversification, but I use a version of the Kelly Formula in the following way:
1) I use a cash position as my bankroll portion that is not ‘bet’ in the stock market for the next annual period.
2) if my stock portion is down at the end of the year, I use the cash to backfill the stock portion back to beginning year level (or as much as possible in case of a larger drawdown).
3) I try not to sell stocks to rebalance. Mental model is to accumulate shares, not to sell them and limit future compounding.
4) I try to limit my cash bankroll to a max 20%. This level could backfill a 25% drawdown (20/80)
5) the cash is tied to the stock investment and is intended to be deployed and not held. It’s really a form of value averaging.
6) once deployed the cash bankroll portion is replenished with new savings
7) as the stock portion has gotten larger, it’s more difficult to replenish cash when there’s a larger drawdown. For example after the COVID 35% S&P drawdown in March 2020, I deployed all the cash, but have found it difficult to replenish without selling stocks. An IRA has limited contributions so I have to trimmed some positions that have gone parabolic to replenish the reserve quicker. I have also sold call options on some positions to generate cash.
8) cash has limited opportunity cost in today’s environment
9) cash’s option value increases with the volatility of the underlying investment.
10) prepositioned cash has served as a psychological hack for me. I actually look forward to drawdowns so I can deploy the cash.
Ultimately, while in the accumulation phase of the life cycle, I’m trying to maximize the compounded returns of my stock portfolio by not selling and backfilling stock drawdowns with a prepositioned cash bankroll. This is in an attempt to limit the volatility drag of steep drawdowns over a long term investment horizon.
Curious on how others have addressed portfolio strategy in the context of mean variance optimization vs geometric maximization?
Grif
