How much should you allocate to Bitcoin in your portfolio?

THE more bullish you are on an investment, the more of it you'd like to own. After taking into account the risk of things turning out worse than expected, investors with some level of risk aversion would moderate their bullishness, and decide their allocation according to these 2 variables.

In equities, there are academic financial models that can determine an optimal allocation, such as the Geometric Brownian motion that can simulate stock price paths, and is used to price equity options using Black-Scholes.

The problem with using such models for crypto, is that during the asset's short life so far, the price-return distributions do not follow these models.

In all my recent research on crypto, I remain unconvinced about it being a store of value, a medium of exchange, digital gold, or the other arguments put forward for how it is a better form of money. However the momentum behind the crypto movement is now strong enough that it has likely become self-fulfilling, and there is a good probability that Bitcoin and the other more established crypto "currencies" like Ether are here to stay. While I remain sceptical about many of the claims about crypto replacing money, blockchain technology offers potential to disrupt many parts of business.

In my search for how a rational investor should allocate to the crypto space, most investors have come to a decision to allocate a small portion of their portfolio, say 1 to 2 per cent. This seems like a sensible allocation given the high volatility. There is also the downside risk that this all ends up being a fad that doesn't live up to expectations, and eventually fades into obscurity like so many other bubbles of the past. And yet, there may be a better way to calculate your allocation.

I came across a paper tackling this exact question by Victor Haghani of Elm Wealth. Haghani uses 2 variables to give an optimal allocation for crypto to a portfolio: the probability of losing your whole investment, and your upside target for the investment. For the examples below, we shall use Bitcoin to keep things simple, though any investment within the crypto space can be substituted.

We need to fix 1 of the 2 variables, so that we can model the optimal allocation based on the other variable. Since the variability of expected returns will be extremely large depending on the investor's bullishness about crypto, let's begin by fixing the probability of losing your whole investment. For the purpose of our example let's say there's a 50 per cent chance of your crypto allocation going to zero.

I can hear the crypto fans howling in disapproval already.

For those still reading, I believe this is a fair assessment of the downside risk. Bitcoin could fail to live up to its expectations and have its bubble burst and never recover. Most bubbles burst by losing 80 per cent of their value in a couple of years, and never recover.

Interestingly Bitcoin went through this in 2018, though it recovered afterwards to make new highs. There has never been an instance of the same bubble reflating again, so this is a notch in favour of the crypto bulls. The level of interest in this sector among institutional investors also makes me believe that the momentum in crypto has become so strong as to become a self-reinforcing movement.

However there are other ways to lose your whole investment in crypto. Your hard drive could crash and you forgot to back up your personal key, losing all access. Or, you did back it up online, but you got hacked and had it stolen. Or, you wrote it on a piece of paper, and forgot where you put it. Irrespective of your crypto bullishness, the chance of total loss is definitely not zero.

The crypto fanatics who allocate 100 per cent of their life savings to the sector have stopped reading by now. For everyone else, let's model the next variable: your assessment of the gains for the asset in the future.

Let's say you believe the argument that Bitcoin should be worth US$500,000, as ARK's Cathy Wood has predicted. That would be 12.5 times today's price. It would incidentally also be worth more than the amount of gold in the world, so the proponents of the "Bitcoin as digital gold store of value" argument particularly like this price target.

Using these 2 variables the optimal allocation would get you to a 15 per cent of your portfolio, which looks high. As you go further and model the whole curve on estimated future returns, an interesting picture emerges. For extremes of crypto bullishness (let's say a 1,000x return, i.e. Bitcoin at US$40 million), paradoxically your allocation should actually be lower, all the way down to around 3 per cent of your portfolio.

To conceptualise the optimal allocation being lower the more bullish you are in the space, if there's a not insignificant chance of total loss, and the return from this investment will give you more money than you and your next generations will ever need, there's no reason to risk a large part of your assets on this view.

Modelling the allocation gives a result that looks like a normal bell-curve distribution with a large right-side fat tail, where the levels of expected return go to extremely high levels. Using our 50 per cent chance-of-ruin estimate, the peak optimal allocation is 17 per cent of the portfolio, equivalent to an expected return of 5 times your investment. If you expect Bitcoin to merely double, your allocation would be zero. Why risk anything when you also have a 50 per cent chance of losing it?

Here's another interesting finding, which will make some institutional allocators think twice. If you're putting a 2 per cent allocation to crypto in your portfolio, and you agree with the 50 per cent probability of losing the investment, then your allocation is suboptimal, because it works out to an expected gain of only 30 per cent in your holding on the conservative side, and over 2,000 times on the bullish side, as every allocation has 2 estimates of upside return.

I think it's safe to say that anyone who has allocated 2 per cent expects a higher return than 30 per cent on their investment, and yet is not as bullish as to expect a Bitcoin price of US$80 million per coin.

Michael Saylor, chief executive officer of Microstrategy, has gone "all-in" on Bitcoin, even issuing bonds to fund the purchases. He predicts Bitcoin will be the first US$100 trillion asset. If this were to happen it implies a Bitcoin price 120 times higher than today. His optimal allocation should therefore be 8 per cent, instead of his 100 per cent allocation. Haghani's model gives a better statistics-based model to calculate your optimal allocation based on your own personal estimates of crypto's upside and risk.

The writer is co-founder of AL Wealth Partners, an independent Singapore-based company providing investment and fund-management services to endowments and family offices, and wealth-advisory services.