Portfolio Sizing: Master the Art for Optimal Returns

Portfolio sizing, or how much of your total net worth should be exposed in a single investment, is a frequent topic of investment debate. Often the single most important decision an investor makes, yet it is not well understood by many retail investors. Sizing and the rules, upon which adding and trimming (i.e., buying and selling) from an investment are made, are perhaps the most influential factors in what drives modern equity markets. 

To illustrate the significance of portfolio sizing and the rules upon which the three cardinal decisions of investing revolve, should we buy, sell or hold on a given position, please assume the following two simple rules:

1) 25% of the portfolio in any given investment

2) Rebalance once, quarterly

If we were to invest our portfolio as follows, with the related performance outcomes, we could find ourselves potentially bankrupt in 10 years.

Year 1: Starting point $400 divided across four assets, 25% each

25% - Asset A: $100

25% - Asset B: $100 

25% - Asset C: $100

25% - Asset D: $100

Year 1 Q1 performance

Asset A: $100 | Loss 50% = $50

Asset B: $100 | Gain 50% = $150

Asset C: $100 | Loss 100% = $0

Asset D: $100 | Gain 100% = $200

Year 1 End of Q1 rebalance: $400

Asset A: $50, so buy $50 more = $100

Asset B: $150, so sell $50 = $100

Asset C: $0, so buy $100 more = $100

Asset D: $200, so sell $100 = $100

Year 1 Q2 performance

Asset A: $100 | Loss 50% = $50

Asset B: $100 | Loss 50% = $50

Asset C: $100 | Loss 50% = $50

Asset D: $100 | Gain 10% = $110

Year 1 End of Q2 rebalance: $260

Asset A: $50, so buy $15 more = $65

Asset B: $50, so buy $15 more = $65

Asset C: $50, so buy $15 more = $65

Asset D: $110, so sell $65 = $65

Year 1 Q3 performance

Asset A: $65 | Loss 20% = $52

Asset B: $65 | Loss 20% = $52

Asset C: $65 | Loss 20% = $52

Asset D: $65 | Gain 20% = $78

Year 1 End of Q3 rebalance: $234

Asset A: $52, so buy $6.50 more = $58.50

Asset B: $52, so buy $6.50 more = $58.50

Asset C: $52, so buy $6.50 more = $58.50

Asset D: $78, so sell $19.50 = $58.50

Year 1 Q4 performance

Asset A: $58.50 | Gain 5% = $61.425

Asset B: $58.50 | Loss 50% = $29.25

Asset C: $58.50 | Loss 50% = $29.25

Asset D: $58.50 | Loss 50% = $29.25

Year 1 End of Q4 rebalance: $149.175

Asset A: $61.425, so sell $24.13 = $37.29

Asset B: $29.25, so buy $8.04 more = $37.29

Asset C: $29.25, so buy $8.04 more = $37.29

Asset D: $29.25, so sell $8.04 = $37.29

At the risk of boring the reader exhaustively with the math, let’s pause and assess our situation after one year of this hypothetical. We started with $400 and ended with $149.175 which reflects a loss of $250.825 or 62% if we rebalance once a quarter.

How can we lose 62% if we limited our investment size to 25%? 

Let’s start by running a simulation with the same quarterly performance, but without quarterly rebalancing. In other words, what would have happened to the portfolio if we didn’t adjust it throughout the year?

We would have ended up with $183 at the end of Q4, reflecting a lost of $217 or 54%. So that tells me that the rules around rebalancing also matter; in some situations the results can improve with quarterly rebalancing while in other circumstances the results are hindered.

Imagine a situation where one investor puts it all on one single investment, one farm so to say. This investor has literally and figuratively bet the farm on that one asset’s fortunes, good or bad.  Imagine that asset was Asset C from the example above; the investor would have been wiped out (i.e., bankrupt) at the end of Q1. 

I researched optimal position sizing and the results were inconclusive. Too many variables impact the results, and the future performance of those same assets is not guaranteed. Go ask the company specializing in horse saddles in 1860 New York City or the coal home delivery service located in Pennsylvania in 1910 how their business is today. 

What I am comfortable concluding based on my personal analysis and hypothetical modeling, is that limiting the position size is a highly personal decision and may reflect other non-disclosed factors such as the agency bias of the individual making the investments (i.e., will they suffer the losses or is that the client’s problem?). For the knowledge I have at this time, I believe the following position size limits and rules will allow me to maximize my returns will managing my risk:

Proposed position sizing rules:

1. No more than 5% of net worth in any specific investment (e.g., Equity shares of Nvidia).

   1. Limits a total loss to 5% due to idiosyncratic risks unique to that particular entity but not spread across the industry.

2. No more than 20% of net worth in any specific investment class (e.g., Equity shares of Semiconductor industry)

   1. Limits a total loss to 20% of net worth in the event an industry-wide impact occurs.

3. Annual rebalancing versus quarterly, monthly, weekly or daily

   1. Allows for an asset on the rise, appreciating, to continue to run up from a momentum perspective as the belief is that momentum cycles tend to persist longer than a quarter.  While market dynamics change, I will continue to explore longer duration rebalancing windows to determine if a longer time horizon of 2 years or 5 years is more accretive. 

4. Total net worth, estimated with your own mark-to-market (MTM) values

   1. Use the percentages including your total net worth, which may be comprised of multiple asset classes outside of traditional markets (e.g., private debt, real estate), using your own estimate of the value of the assets. Mark-to-market (see blog post on the topic) is the price of an asset based on what the asset is actually trading at, not the advertised price. In other words, I can offer to sell you my car for $1MM and say that is the price. But it is a Toyota Land Cruiser, and the MTM says otherwise, with that type of truck trading at multiples far lower. So the value in your net worth calculations should reflect your best estimate of reality and in most cases, a ‘haircut’ is needed on the asset value.