by Lars Kroijer
Bullshit in, bullshit out
One of the things I disliked about investment banking was building massive 50-page Excel models, outlining projections of companies and industries. We would often have little to go on in terms of projections other than short analyst reports which we would use to extrapolate all sorts of data to get 5–10 year projections with all the bells and whistles. We would call this ‘bullshit in, bullshit out’, suggesting that the financial models were only as good as the assumptions we put into them.
As with the large investment banking financial models, optimal portfolio theory is subject to getting our assumptions right. You probably noticed how casually the theory suggested that you input the expected risk and return for individual securities, and the correlation between them, and voilà, the efficient frontier and the tangency point are revealed. Or rather for about £50 you can buy software that will do that for you. But the world is obviously not that simple. Ask 10 market participants about the expected risk and return over the next year on Apple shares and its correlation with Microsoft, and you will get 10 different answers. Now ask the same people to do the same thing for all listed stocks and they will tell you that you are crazy – it’s not realistic to have this kind of expectation for more than a small portfolio of shares, and besides, risk and return expectations, and correlations, change all the time. It simply can’t be done.
The beautiful shortcut – follow the crowd
But here is the beautiful thing. If you generally believe in efficient markets, you don’t need to worry about the portfolio theory above or collecting millions of correlations and thousands of risk-return profiles. The market’s ‘invisible hand’ has already done all that for you. We don’t think we are able to reallocate between securities in such a way that we have a higher risk/return profile than what the aggregate knowledge of the market provides. Buying the entire market is essentially like buying the tangency point T.
To some people it will seem like too bold an assumption that capital has seamlessly flowed between countries and industries in such a way that world markets are efficiently allocated. But if we asked: which country/industry/company is it that you want to reallocate money to/from contrary to the combined information and analytical power of millions of investors allocating trillions of dollars, and why? Accepting that investing internationally gives us greater choice and diversification than only investing in one country, we need to figure out some way to allocate between those choices. If we picked the countries/industries/companies on anything other than their relative market sizes we would essentially be claiming we knew something more than the markets.3
You can of course disagree with all of this and make claims like ‘Microsoft will go up 20% next year regardless of the market and there is almost no risk that I am wrong’. Of course you might be right, but you are also clearly claiming an edge in knowing or seeing something that the rest of the market does not. Do that consistently and you’ll be rich.
Going back to the example of having only the choice of the riskless investment and investment A, that is essentially where we end up. If we replace investment A with the world equity portfolio, and replace the riskless investment with the minimal risk asset, we have moved on from the world of portfolio theory to the real world with investments we can actually implement. We will see later that the minimal risk asset depends on the base currency of your investments.
Investment A in the chart, therefore, consists of many thousands of underlying equities from all over the world in the portfolio (see later). By combining the minimal risk asset and A (world equities) in various proportions we choose various risk/return levels in the most efficient way, from minimal risk to the risk of the world equity markets, or greater than that if we borrow money. Point T is already the tangency point, or optimal portfolio, and we don’t think we can reallocate money between the many securities in such a way that we end up with better risk/return characteristics (see Figure 3.7).
Figure 3.7 Combining the minimal risk asset and world equities
Later, when we add other government and corporate bonds, we will see that this is akin to when we added the possibility of investment B earlier. While adding a bit of complexity to the portfolio, the other government and corporate bonds enhance the risk/return profile of the whole portfolio.
The best theoretical and actual portfolio
The rational portfolio is a compromise: a compromise between what we would like to create in a theoretical world and what is available practically. In an ideal (theoretical) world we should own a small slice of all of the world’s assets to maximise diversification and returns. This clearly is not possible in reality, but the rational portfolio is a very good simplification that we can actually implement. Because the asset classes of the rational portfolio have active and liquid markets for the pricing of thousands of individual securities, we don’t need any specific insight to select securities in those markets. And because government bonds, equities and corporate bonds give a very good representation of the world’s assets, a portfolio representing those asset classes is a very good simplification of what we should ideally be striving for in a portfolio. We can accept the premise that market forces have set a price on individual securities and the aggregate market at a level that is consistent with the risk/return characteristics of that asset class. Because equities are riskier, we get higher expected returns, etc. For other investments left out of the rational portfolio there is typically not a liquid and efficient market to set prices for the individual investments, so someone without an edge is unable to simply buy into the whole asset class and expect to get its overall risk/return.
So there is no theoretical inconsistency in being a rational investor – on the contrary. We don’t think we know any better than the market about the risk/return profiles of individual securities or how they move relative to one another. By pricing securities, the market effectively incorporates the views of thousands of investors and presents us with the results of the market as it currently stands.
So what is ‘the market’?
In equities, the market has often meant your local stock market. And if you invest in your local index in a cheap way you are doing better than by picking individual stocks or active mutual funds, but not as well as you could be. You could be picking a much broader geographical range of the world stock markets in proportion to their values.
So only publicly listed equities?
In order to keep things simple, we typically refer to the markets as the listed equity markets. If you invest in a combination of the minimal-risk asset and broad-listed equity markets in a cheap and tax efficient way, you are doing better than most. If you are willing to add a bit of complexity there’s a lot of merit in adding other government and corporate bonds to your portfolio (see later).
Summary
The ‘invisible hand’ of the markets has optimised the values of the investments available. We should celebrate this simplicity and buy the whole market. We don’t think we can reallocate between securities to get a better risk/return profile.
Combine the world equity markets with investing in the minimal risk asset to get to the kind of risk profile you want.
The markets could mean for you only a broad range of equities, but adding other government and corporate bonds has a lot of merit.
1 An important point on portfolio theory and the minimal risk asset that will be discussed later. In accepting that the minimal risk asset is not entirely without risk the line between it and investment A is theoretically not straight, but a curve. Depending on how the minimal risk asset and investment A move relative to each other you might actually end up in a situation where the lowest risk combination of the two is not the 100% minimal risk asset, but instead has some investment A in it. For the purpose of simplicity, I have ignored this possibility.
2 This leveraged portfolio assumes that we can borrow money at the riskless rate to invest in more of the T combination, which we can’t. In reality, the cost of borrowi
ng would be higher and the line would be flatter to the right of T than it would be to the left of T, to reflect this. If you were unwilling or unable to borrow money, the optimal portfolio at higher risk levels than T would consist increasingly of A and would be represented graphically on the curved line from T to A.
3 We are here assuming that capital can flow easily between countries and industries, which is increasingly a fair assumption.
part two
The rational portfolio
chapter 4
* * *
The minimal risk asset – safe, low-risk returns
Buy government bonds in your base currency if credit quality is high
This chapter is about finding the lowest-risk investment as the base on which a riskier portfolio can potentially be built. Your choice depends on currency: for a sterling-denominated investor, short-term UK govenment bonds are a good choice. As discussed previously, there is probably no genuine riskless security in the world today, but the probability that the UK government will default is very low; thus minimal risk.
By comparison, a US-based investor buying short-term UK government bonds would have the same security of getting his principal back, but would incur currency risk as the GBP/USD exchange rate fluctuations add risk. So if, for example, the UK bond promised to pay the investor £101 a year hence for a £100 investment today, both investors are equally certain of receiving £101, but while the £101 would always be £101, the US dollar value of that amount could fluctuate quite a bit and is thus more risky. The US investor would therefore be better served by owning short-term US government bonds that are of similar credit quality to the UK government bonds where his returns would be independent of currency risk.
If your base investment currency is one where the government credit is of the highest quality, those government bonds will generally be a great choice for your minimal risk investment. While most investor’s base currency is obvious (sterling for UK investors, dollars for US ones, etc.), and currency risk is a risk you would rather avoid, your base currency can also be a mix of currencies. It is essentially the currency that you think you will one day need the money in. So while I may live in the UK and probably have the majority of my future expenses here, I also spend a lot of time (and money) in Denmark, the eurozone and the US. Also, I may have future expenses for my children’s education outside the UK, or my wife and I might live or retire abroad one day. By having my base currency as a mix of several currencies, albeit dominated by sterling, I will better match my future cash needs and leave myself less at risk of being caught out by a falling currency with potential expenses in other currencies.
Today there are three major credit agencies that rank the creditworthiness of bonds, namely Moody’s, Standard & Poor’s and Fitch. Here is how those agencies rate long-term bonds.
The credit agencies were widely discredited after 2008 when they wrongly gave high ratings to all sorts of sub-prime garbage, but in general they give you a good indication of the credit quality of a country’s bonds.
Credit ratings change frequently. As you consider adding your minimal risk asset, you can see the latest credit ratings on Wikipedia by searching for ‘List of countries by credit rating’. If the government credit of your base currency is listed here as AAA you have an easy choice for your minimal risk asset. With the adverse environment of government debt and deficits in recent years, the list of AAA-rated countries from all agencies has shortened. That said, if your home base currency offers AA or higher-rated bonds then it would be sufficient to accept those as your minimal risk asset. If we only accepted bonds with the highest rating, at the time of writing that would exclude bonds from major economies like the US, Japan and France, which is neither practical nor desirable for many investors (the UK was also recently downgraded from the top rating by Moody’s and Fitch). While there is obviously a reason for these countries losing the highest rating it is worth noting that the financial markets trade the bonds at real yields that are among the most creditworthy in the world in any currency.
If your base currency is one without a highly rated bond available, you face a tougher choice. For all their undoubted economic successes over the past decades countries like Brazil, Mexico and India do not have highly rated government bonds (all approximately BBB-rated at the time of writing). As a Brazilian you could buy Brazilian short-term government bonds which would not be minimal risk or highly rated government bonds in one or a couple of foreign currencies, although this would involve a currency risk. Depending on the credit rating of your base currency government you may choose to take the credit risk of the domestic government bonds instead of taking the currency risk of highly rated foreign bonds, or perhaps even keep money in cash deposits in the local bank if that is considered a superior credit option to domestic government bonds (see the box on pages 49–53).
Older people in certain parts of the world, including Brazil, undoubtedly remember times of domestic economic turmoil and the thought of buying local government bonds as their minimal risk asset will seem like heresy. And they are right. These investors do not have essentially risk-free bonds in their local currency, however far the government has come. Perhaps one day the credits of these governments and many like them will grow in esteem to the point that they become the lowest-risk bonds in the world, but not today. In the past, many investors with a less-creditworthy domestic government essentially made their base investment currency the US dollar and would buy US government bonds for their base currency.
While the lower credit ratings of some government bonds mean that the bonds yield more, this is not a good reason to have them as your minimal risk or safe asset. As discussed in the next chapter, if you want to add returns to your portfolio you can do so by adding broad exposures of equities that have the added benefit of both being geographically diversified and adding expected returns.
Perhaps diversify even the very low risk that your domestic government fails
Investing in sub-AA credit ratings is a question of degrees. Some investors would be happy to invest in their BBB-rated local currency government bonds whereas others would rather invest abroad with currency risk than have an AA domestic-rated government bond. The choice partly depends on your situation and sensitivity to currency risk versus domestic credit risk. For those inclined to accept sub-AA domestic government bonds as their minimal risk asset I would encourage you to think about what else would happen in your portfolio if your domestic government defaulted. In most cases, a domestic government default would have a catastrophic effect on your portfolio and general life.
If you had diversified some of the domestic risk away by having your minimal risk asset as highly rated foreign bonds, such as German/UK/US government bonds, then you would at least have some respite when the domestic calamity hit. Also, some investors consider that having all your minimal risk assets invested in the bonds of just one government, however creditworthy, is a bad idea. Those investors argue that while the government bonds of Britain or Germany are highly rated today there is always some risk that they could fail, perhaps even spectacularly and quickly.1 Because of this eventuality investors should diversify their minimal risk asset into a couple of different, highly rated government bonds, even if this means taking a currency risk for those bonds that are not in your base currency. My view is that if you are invested in government bonds that are among the most highly rated in the world the probability of a sudden default is so low that for practical purposes it is a risk you could feel safe taking.
Here are some recommendations for minimal risk assets depending on your base currency:
So your minimal or ‘safe’ asset is not necessarily your domestic government bond. Consider a Spanish investor who is after the lowest risk asset, and does not want to take a currency risk. This investor should not be buying Spanish government bonds that are quite lowly rated, but instead should buy German government bonds that are also euro denominated. If this investor did not want the minimal risk to be the bonds of j
ust one government he could diversify by either adding other euro-denominated government bonds or accept the currency risk with highly rated non-euro government bonds.
In most countries there are domestic bonds related to the sovereign issuer, such as government-guaranteed regional, city or municipal bonds. Those and similar bonds could be reasonable alternatives as minimal risk assets, particularly if there are tax advantages to investing in them. However, make sure that the guarantee is bulletproof even in distress. If you get a superior yield from these alternative bonds compared to the standard government bonds, you are probably taking additional credit risk. Also be careful in thinking that adding these kinds of bonds provide you with additional safety; they are typically a poor diversifier of risk as they tie back to the same creditworthiness as the domestic government bonds.
Matching time horizon
In the discussion above, short-term bonds are the minimal risk asset. This is because longer-term bonds have greater interest risk (the fluctuation in the value of the bond as a result of fluctuations in the interest rate). Consider the example of a one-month zero-coupon bond and a 10-year zero-coupon bond that trade at 100 (zero-coupon bonds don’t pay interest, only the principal back at maturity). Now suppose annual interest rates go from zero to 1% suddenly. What happens to the value of the bonds?
