## “With inflation at 7.5%, you lose half your money in 9 years. The only way to outperform that consistently, that I have found, is crypto. Just this year I’ve already lost half my money.” – RCM via Twitter

## “With inflation at 7.5%, you lose half your money in 9 years. The only way to outperform that consistently, that I have found, is crypto. Just this year I’ve already lost half my money.” – RCM via Twitter

## “With inflation at 7.5%, you lose half your money in 9 years. The only way to outperform that consistently, that I have found, is crypto. Just this year I’ve already lost half my money.” – RCM via Twitter

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 two 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 of 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%. This seems like a sensible allocation given the high volatility, and also the downside risk that this all ends up being a fad that doesn’t live up to expectations, to eventually fade 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 two 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 one of the two 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% 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% 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 by institutional investors is also what 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 backup 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% 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 $500,000, as ARK’s Cathy Wood has predicted. That would be 12.5x 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 two variables the optimal allocation would be a 15% 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 $40 million), paradoxically your allocation should actually be lower, all the way down to around 3% 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 that 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% chance of ruin estimate, the peak optimal allocation is 17% of the portfolio, equivalent to an expected return of 5x your investment. If you expect bitcoin to merely double, your allocation would be zero. Why risk anything when you also have a 50% chance of losing it?

Here’s another interesting finding, which will make some institutional allocators think twice. If you’re putting a 2% allocation to crypto in your portfolio, and you agree with the 50% probability of losing the investment, then your allocation is suboptimal, because it works out to an expected gain of only 30% in your holding on the conservative side, and over 2,000x on the bullish side, as every allocation has two estimates of upside return. I think it’s safe to say that anyone who has allocated 2% expects a higher return than 30% on their investment, and yet is not as bullish to expect a bitcoin price of $80 million per coin.

Michael Saylor, CEO of Microstrategy, has gone ‘all-in’ on bitcoin, even issuing bonds to fund the purchases. He predicts bitcoin will be the first $100 trillion asset. If this were to happen it implies a bitcoin price 120x higher than today. His optimal allocation should therefore be 8%, instead of his 100% 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.

**By LEONARDO DRAGO**

**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 to accredited individual investors.**