*First things first, a disclaimer is probably needed. It is important to keep in mind that I am not advocating piling a bunch of money into random start-ups at any valuation, which is a recipe for disaster. Instead, I am trying to shed some light on something I find a lot of people aren’t fully aware of, and something which a lot of people (and especially young people) could benefit from*.

It is fairly clear that the last couple of years have largely been dominated by the Silicon Valley start-up scene. Eye-watering valuations for companies with zero profit, and sometimes zero revenue have seemed to become the norm, and in the process making many people extremely wealthy (at least on paper). This is what most people think of when you start talking about start-ups. A company created by a couple of tech geeks that venture capital investors hope will turn into the next Unicorn. It is important to note that this is NOT what I am referring to when I talk about investing in start-ups. I don’t necessarily concern myself with the start-ups that we all read about in the news because:

- There is pretty much zero probability that I would get the chance to invest in a potential tech unicorn, as you have to be VERY well connected and
- Even if I did get the chance to invest, the fact that they are asking me for money is not a good sign. If a business plan of a tech company that aims to become the next Instagram comes across my desk, I can’t even imagine the amount of people that have already said no, especially given the amount of money chasing anything that has tech in it

It’s not to say they aren’t interesting, but they aren’t relevant to me as an investor. What is relevant to me is a smaller business that has a clear exploitable niche and high operational leverage due to low fixed costs. But I will go more into detail on how I look at making an individual investment in a future article.

There is one final note I want to make with regards to the large unicorns that are constantly in the media before I carry on with the real purpose of this article. The headline valuations of a lot of these start-ups are based on a somewhat flawed system, and by flawed I mean in terms of finding a fair market price. Maybe flawed is the wrong word, and biased is more appropriate. For a regular stock that is traded on a public market, for example GOOGLE, the price is set via an interaction of buyers and sellers. The equilibrium price at any point is one that balances the demand and supply of the market participants. If the price gets too high then supply will overwhelm demand and the price decreases (and vice versa). However, the headline valuation of 20 billion reported for a start-up is set by one, or a small group, of investors in a bidding process for a small investment (small relative to the headline valuation). A 20 billion headline valuation can be the result of a single investor putting in 100 million for a 0.5% ownership stake. So yes, someone thinks that the company is worth more than 20 billion; however, instead of a price determined by balancing supply and demand, the headline valuation is by design set by the most optimistic buyer. In addition to this, all we see is the headline numbers of the investment, whereas in reality there are a lot of provisions that come with the investment that often times protect the investor. For example, if an investor buys a 0.5% stake for $100m in regular equity with none other provisions, then yes he is valuing the company at $20b. However, if the investor is buying a 0.5% stake with a claim on any assets of the company, then he isn’t valuing the company at $20b, as he is in effect senior to other shareholders without that protection. This isn’t necessarily relevant to the rest of the article, but I find it is something a lot of people don’t necessarily realize.

Detour aside, there are three primary reasons I invest in start-ups as part of my broader investment portfolio. The first two are fairly generic, obvious, and depend on the individuals risk tolerances and investment opportunities, and so feel free to skip them if they seem boring and dry. The last one is something that can benefit pretty much anyone (as long as they are a UK resident).

**Reason 1: Adding uncorrelated assets to an investment portfolio is the only true free lunch**

This is a more specific way to state one of the oldest investment adages out there, that “diversification is the only true free lunch there is”. Well, some people also argue compounding is but that is a story for another day. Most people are aware of the need to diversify their investments. Even when I interview university students for internships and graduate positions the first thing 90% of them say when I ask how they would invest 100m is that they would diversify. Most people understand that unless you can watch your basket like a hawk, you don’t want to place all your eggs in just one. However, most people I talk to also misunderstand the adage slightly, and that misunderstanding can lead to sub optimal investment returns.

Essentially, the objective of diversification is to achieve the same portfolio return but taking a smaller amount of risk. Mathematically this is often times measured by what is known as a sharpe ratio, where risk is represented by the standard deviation of a portfolio. Standard deviation is essentially how far away individual occurrences are from the average. So if you have an investment that has an expected return of 10%, but can be up 50% or down 50%, that has a higher standard deviation than one that can be up or down 20%.

Now standard deviation is only a proxy for risk and I will discuss why a high standard deviation can actually be a good thing in the next section, but for now, it’s safe enough to assume for the majority of people, for a given return, they would prefer a lower standard deviation in their portfolio. This is mostly due to the fact that on an overall portfolio basis over the course of 20+ years, an individual needs to avoid large drawdowns, even if it comes at the expense of giving up the extremely large upside. For example if you have two portfolio’s, both with an expected return of 5%. Portfolio A gives a steady return of 5% every year, whereas Portfolio B can be up or down 50% in any given year, but also with an expected return of 5%. For the majority of people, Portfolio A is the obvious choice, as the steady return makes planning easier (i.e. mortgage, school fee’s, retirement savings etc), and avoids the catastrophic scenario’s where you are basically wiped out. In economics speak, most people’s utility functions aren’t linear, as they need to avoid the catastrophic downside scenario more than they want the huge upside return scenario. So therefore we can make the statement that on a portfolio level over a long period of time, people should try to maximize their sharpe ratio.

This is where diversification comes into play, and why it’s so often labelled as the only free lunch (and why everyone preaches it). Diversification allows you to achieve the same return but with a lower standard deviation. Let’s take a simple example, where you have 20 uncorrelated assets that you can invest in, and each of these assets can be anywhere between -2% and 5% in any given year (and with a uniform distribution in between). You can choose how many of these assets to split your money across. Running a simulation of 20,000 trials, we get the below portfolio results:

So as you increase the number of assets, the standard deviation of your portfolio drops (red line as you move left to right) and as the expected return is constant your sharpe ratio by definition increases (the blue line going from left to right). So whereas for 1 asset you get approx. 1% return for 1% of standard deviation, if you split up the investment into 20 assets, you get 15% of return for 1% of standard deviation.

Now the part that most people get wrong (and even a surprising amount of interview candidates with finance backgrounds from top universities): the key to the above is the fact that the assets have zero correlation between each other. The problem is most people confuse zero correlation with negative correlation. The thing I hear all the time is this: “I have XYZ stock, but I also have ABC stock that I expect to do well if XYZ drops and so I’m diversified”. That isn’t zero correlation but a negative correlation. Let’s take this example into the extreme. You have two assets, both can be up or down 5%, but they are perfectly negatively correlated, so if one is up 5%, the other is down 5%. Most people will agree that the return of this portfolio is by default 0. So why would you invest in this portfolio? All that you accomplish is paying transaction costs. A negative correlation is more of a hedge than a diversification. And if you want to hedge (i.e. take less risk) then why not just reduce position size? Negative correlations are useful for two reasons:

- Isolating risk exposure. Lets say you have a company that produces both cars and computers, and a second company that makes just cars. Now you believe that the computer market will take off for whatever reason, but don’t want to be exposed to the car industry. Here you could buy shares in the first company and sell short the shares of the second company. These two positions would be negatively correlated, but would be a way to isolate the risk exposure you want
- You have an investment in an asset that is very illiquid so to get out you would have to incur large transaction costs and you would have no certainty that you could get back into the position. However, you believe that over the next year the price of the asset will fall. Here you could use a negatively correlated, more liquid instrument to trade this view. For example, you own a property but you think the housing market will crash over the next year, but then rebound. Instead of selling the house and trying to buy it back in a year which would be a massive pain, you could short some sort of property stock or housing index

Note that both of these reasons do not deal with diversification, but rather more tactical shorter term trading purposes. If you are just looking to take less risk, instead of having two negatively correlated assets, why not just have less of one asset?

For diversification, the key is to get as close to zero correlation as possible. This means that the returns of your assets in the portfolio are completely independent from each other. Now in the financial world, it’s extremely hard and borderline impossible to find zero correlated assets. And even if you do find assets that show zero correlation in a normal state of the world, all correlations tend to go towards 1 in a crisis (as most crises are liquidity based, so when everyone needs cash, all assets are sold off), and so you lose the zero correlation when you most need it.

So how does this tie back into start-ups (I apologize for the large detour)? I personally believe that adding a start-up allocation to my portfolio gives me some additional diversification. Personally, a lot of my portfolio is tied up in the mainstream financial sector: my pension is invested across global equity markets, my future salary is tied to the performance of the broader hedge fund industry, my deferred compensation is invested in the fund itself. So when it comes down to it, a lot of my investments are very positively correlated. Now the argument can be made that start-ups are extremely correlated given that when funding dries up due to an economic crises then start-ups will have zero access to credit. That is true, and that ties back into the concept of finding start-ups that have a high degree of operational leverage and so need limited external funding. I try to make sure that the start-ups I look for can survive on a very limited funding base. I believe that having this allocation in my portfolio of smaller niche companies that don’t require a lot of access to funding present somewhat of an uncorrelated asset to my other investments.

**Reason 2: Not all volatility is created equal in a non-linear utility function**

At first this is going to sound hypocritical to some of the points made in the previous paragraph, but its more expanding the framework rather than discrediting it. The utility function is an important concept that explains what on the surface seem like irrational decisions made by individuals. The general idea is that the utility to an individual is not 1 for 1 to the monetary value at stake. For someone with savings of $100k, the pain of losing $100k is likely greater than the benefit of gaining $100k. Therefore if he was faced with a 50/50 bet where he can either win $100k or lose $100k, he would not want to take that bet, as even though on a purely mathematical expected value basis it’s a neutral bet, to him it actually presents negative utility. Therefore the absolute amounts of the payoffs are important. If someone offered me a 60%/40% bet in my favour to win or lose $100k, I wouldn’t take that bet. However, if someone offered me a 60%/40% bet to win or lose $100, then I would take it all day long. The idea of utility functions explains why people pay for insurance or buy lottery tickets. In the former the costs of a loss are great enough that they are willing to pay above the odds to protect themselves. In the latter, when the reward is huge compared to the cost, and the cost is tiny compared to overall savings, then the cost gets rounded down to 0.

This leads to the point at hand. Let’s say you come across a guy that is offering a bet, and you have to choose to take one side of the bet. In the bet you gain/lose $10 with 99% probability, and lose/gain $990 with 1% probability. Now taking either side has the same expected value ($0) and same standard deviation ($99.5), so presented with just those two statistics (mean and standard deviation), you would be indifferent as it looks like the same bet. However, presented with the actual payoffs, most people would rather lose $10 to gain $990 than the other way around.

Note that in the previous section, we measured the efficiency of returns via the sharpe ratio (expected return/standard deviation), to get a sense of return per risk taken. This approach works if you are treating standard deviation (or risk) in a symmetrical sense. However, in the real world it gets more nuanced than that as we saw with the simplified bet examples. As people show everyday all around the world when buying lottery tickets, sometimes it makes sense to pay above expected value for high standard deviation in the right direction.

Start-ups in my portfolio provide this sort of skewed upside. Most start-ups go bust, but at the same time the upside % return on money invested is potentially extremely high. I look at the start-ups I invest in the same way as I view cheap lottery tickets, where I both expect a positive return, and get a benefit from the high standard deviation to the upside. I am happy to spend 5-10% of the money I save every year and stick it into a start-up, because in the grand scheme of things losing that money won’t kill me, and the upside is potentially very significant. In other words, my lifestyle doesn’t change if I save a bit less every year, but it can change dramatically if one of these investments pays off.

Essentially, when talking about risk, it encompasses both the risk of losing and making money, and I don’t mind carrying the risk of making money.

**Reason 3: The tax breaks available in the UK create a great safety buffer**

One thing that a lot of people I talk to don’t realize is that there are government schemes set up in the UK that provide tax relief for start-up investments. The reason is simply to act as a subsidy to promote investment. The tax relief set up under the Enterprise Investment Scheme (EIS) provides the three following benefits:

- 30% can be offset against income tax paid
- No capital gains tax
- Loss relief against income tax paid

So how does this work in practice? Essentially, if you invest $10k in a start-up that is eligible under the EIS scheme (the company needs to meet certain criteria with regards to business area, size etc), then you can claim 30% of that investment against tax you have paid that year (or the previous year). So if you have paid more than $3k in tax, then you get a check from the HMRC for $3k. Therefore you are essentially able to invest $10k for the price of $7k. In effect, if in 3 years (length of the scheme) the company has not changed in value, you have had a return of 43%.

In the case you experience a loss on the investment; you can then offset the loss against income tax as well. So if you are in a 35% tax bracket for example, and you invest $10k, you have $7k of capital at risk. If the company goes bankrupt and your stake is worth $0, then you can offset 35%*7k = $2.5k versus income tax you have paid.

This is a huge tailwind, and as long as you have some confidence in your ability to find good ideas to invest in then it’s potentially very lucrative.

So let’s throw some numbers around it to make it a bit more tangible. Imagine you believe you can identify investments that have a 1/3 chance of failing (going to zero), 1/3 chance of being unchanged and 1/3 chance of doubling in value. By definition without the tax relief this is a zero expected return investment. However, when we incorporate the EIS relief this changes the picture significantly:

So in a loss, with EIS relief instead of being left with nothing, we are left with the initial tax relief ($300) and the 35%*700 = $245 of additional relief (so a total of $545). If it stays unchanged we have an asset worth $1000 plus the $300 of tax relief we received. And if it doubles we have $2000 plus the $300 of relief. Therefore we have an expected return of $382.

Making the example a bit more tangible to give an idea of how much difference this makes in the grand scheme of things. Let’s say you have the opportunity to invest $1000 each year into a start up with the above return profile (i.e. without tax relief an expected return of $0). Your other option is to invest in something that gives a steady 5% return. Note that I am making several assumptions that make this fairly skewed against the start-up investment:

- A risk free alternative return of 5% is very high
- I am assuming a fixed start-up investment of $1000 per year, and any payoffs from start-up investments along the way are reinvested at the 5% rate of the other investment opportunity, rather than funnelled back into start ups
- I am assuming that the start-ups invested in have an expected profit of $0, whereas in reality I would only invest in projects where I believe in my base case I can make 5x my initial investment

So if we assume for the next 20 years we invest $1000 each year in a start-up, and running 10,000 monte carlo simulations, the following is what our portfolio value would look like after 23 years (23 years as the last start-up investment made in year 20 we are assuming pays off after 3 years).

The blue curve is the probability distribution of the start-up portfolio, and the green line is the average final portfolio value. The red line is the return of the alternative portfolio where you make 5% per year. So even using our conservative assumptions of a zero expected return investment, the portfolio value is expected to be approximately $46k, on a total cash invested amount of $20k over 20 years, just from the tax relief alone. Also worthwhile to note, in all of the simulations, there wasn’t an instance where you ended up with a portfolio value of less than 20k (the total amount invested over the 20 years).

Obviously this is an over simplistic example, and in reality the default probability is likely higher and the upside is larger, but the message is quite simple. As long as you believe you can find investments that offer some sort of positive expected return, the tax relief available makes start-ups potentially very attractive investments.

**Final note on sizing**

Now start-ups still carry a high risk of loss, which is why sizing is important. Going back to the utility function, I am personally happy to spend 5-10% of my annual savings investing in start-ups, with the actual number depending on foreseeable liquidity needs (travel etc), investment opportunities available, and how much of my existing portfolio is already tied up. Any money you put into this asset class needs to be money you a) don’t need for the foreseeable future and just as importantly b) you need to be able to be ok if this money is lost. It is crucial to remember that you cannot sell your investment easily if you suddenly need the money, and even the tax relief check will take anywhere from 6 months to a year to actually come through. However, given the availability of crowd sourcing and being able to invest in tiny denominations, I don’t see why the majority of people shouldn’t at least explore this in some format.