The Power Law in Venture Capital

Maybe you have heard that returns from venture capital are governed by a "power law". But what exactly is that? When I first read about this I was confused. I have now figured out the technical steps need to convert the general idea of the power law you may see in popular articles into something actually useable. I'll skip those steps and show you what I think is a useable version of this idea. First we need to distinguish between investments that lose money and those that deliver a multiple of one or more times the capital invested. My version of the power law is just for profitable investments with a multiple of one or greater. The equation is:

This says that the probability P that the multiple M is greater or equal to m is equal to the formula on the right, where alpha is the power of the power law. To take an example, if alpha = 1.75 and m is 10, the probability is 0.178 or a 17.8% chance that you get more than a 10x multiple. Conversely, the probability that the multiple is between 1 and 10 is 1-0.178 or 0.822. Remember, that isn't the probability that your investment makes this much money, rather, that if it makes money how likely will it make more than m.

The interesting thing is that for 1 < alpha < 2, the probability of getting a given payoff decreases slower than the payoff is increasing. This means that more and more of the expected value of your portfolio is derived from higher and higher multiples (again for alpha = 1.75):

Expected value is just the product of average payoff and probability. This is why people say that you need to make a lot of investments in venture capital to get good results. If half your investments go to zero, you need to get an average multiple of more than two on the other half to make any money. If you only make ten investments, a 128-256x outcome, which has only a 1.1% probability of happening among your successful investments, probably won't be in your portfolio. 

20 Years of Moomin Valley

Reading Sam's post on 17 years of Financial Samurai, I realized I missed the 20th Anniversary of Moomin Valley! These were the first two posts. In the early years, I posted a lot. Since the GFC and even more since 2012, I have posted less. The nadir was in 2017 (25 posts)–the year after our first child was born. But I still managed a few posts beyond the monthly and annual reports. 2018 was a bumper year for posting and since then, I've stabilized at around 60 posts a year on average. In total there have been 2,270 posts or about 110 per year.

At first, I wasn't sure what I would use the blog for. Mostly, it has been for accountability for myself. I know I need to post about the ups and downs each month. Writing about investments means that you need to think about them. I hoped my wife would read it to learn about our finances, but that didn't really happen. 

More Gold Exposure

I brought my gold exposure back up to 10% of gross assets. But instead of investing in the PMGOLD ETF I invested in the L1 Gold Fund. This is a hedge fund invested mostly in gold mining stocks. I am lumping this in with gold metal as the price of gold is the main driver of gold mining stocks. If the government's capital gains tax changes are implemented, it will be better to have a franked dividend paying fund instead of a gold metal ETF in my personal name.

I also sold some Regal Investment Fund (RF1.AX) and bought some more Pengana Private Equity (PE1.AX). Despite the success of the SpaceX IPO, which is its largest holding, it dropped sharply today! One possible reason is that Pengana is launching a new AI fund, Maybe some people are selling this to buy that?

4% Rule Failure Rate

I have been discussing retirement planning with my brother who is two years younger than me. As a result of these discussions, I have added stochastic investment returns to my projection model as well as the Australian Age Pension (which is means tested) and I increased the planning horizon to 2060 from 2050. Moominmama would be 85 in 2060. Previously, I stress tested the projection by using very low constant rates of return.

Running my baseline spending scenario–linear growth in real spending with stepdowns of 1/6 after each child finishes university–it is very rare to run out of money by 2060. This is defined as negative net worth beside our house. In 100 runs there are no failures.

But if we spend according to the 4% rule, we run out of money by 2060 about 10% of the time, though rarely by 2050. This is using the monthly returns distribution over the last 30 years of the benchmark target portfolio as investment returns. In many more cases, real (2026 dollars) net worth is below AUD 1 million by 2060 and falling fast. If I use our own historical returns–which were very bad before 2012–the failure rate is around 40%. With our returns and linear spending the failure rate is around 25%.  

This graph compares the target portfolio, our track record, Australian shares, the MSCI World Index, and gold:

Spending according to a 3% rule and the target portfolio returns has no failures in 100 runs, though a few near misses. 

So, we need to keep our spending well below 4% or increase returns if we don't want to run out of money.

Things I Don't Invest In

For every investment I do make, there are a lot that I look at and decide against. A recent example that I blogged about is the Pabrai Funds. 

I'm sent more and more invitations to invest in start-ups. One I saw today was Venice AI. Some complicated story about a privacy oriented LLM (but uses resources from other LLMs maybe?) plus two different crypto tokens. I couldn't understand the pitch and deleted it. In general, I like to see some attention to the "economics" - what is the route to profitability. If it is not discussed at all, I tend to pass on the opportunity.

And then there are more mature opportunities including two upcoming IPOs. One is the IPO of SpaceX. CommSec has provided an Australian version of the prospectus. I already have exposure via Pengana Private Equity (PE1.AX) and if I wanted more I could buy more shares in that fund, which are trading at a discount to what the NAV would be with the SpaceX IPO price. SpaceX is their largest holding by far. S&P have decided not to change their index rules to allow unprofitable and new companies to join their indices. NASDAQ on the other hand will be including it in the NASDAQ 100 index very quickly. I am sceptical of the idea that there will be a pop in price at the IPO beyond the already crazy price–the price is near 100 times 2025 sales. With USD 75 billion of shares being issued in the IPO, most people who want them will probably get them? Most IPOs do not perform well in the short term if you buy at the IPO price.

The other IPO I looked at was a new fund from Pengana focusing on 20 private AI related companies–AIX. Bytedance and Handshake are the two seed assets. They will also be investing in "picks and shovels" and applications companies not just LLM providers. But most closed end funds definitely don't trade well following their IPO. My preference is to be invested in related resources (e.g. via Tribeca Global Resources, TGF.AX) and in earlier stage firms that have routes to profitability (see above).

Treasury Wines Investor Day

Two days after I bought into Treasury Wine Estates (TWE.AX), the company had an investor day where they announced that they would focus on luxury and trendy wines and greatly reduce the number of brands and product lines. They also said that they were reviewing their US operations and were getting good sales growth in China–better than other wine producers. Investors were very happy with this presentation and the stock is currently up 13%. I bought another 7,500 shares to get to 17,500.