Chapter 13

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Diversification

The proven way to reduce portfolio risk

‘The only investors who shouldn’t diversify are those who are right 100% of the time.’

John Templeton

We are back to, ‘Do not put all your eggs in one basket.’ It captures the essence of diversification. If you put all your eggs in one basket and drop it, they all break. You are left with nothing (or with a mess). Conversely, if you spread your eggs across different baskets, by dropping one you do not lose everything.

This is the same with investing. Since nobody knows for certain how different assets will perform in the future, spreading investments across various assets reduces risk. When one falls, others may rise.

Diversification works only if different assets behave differently. If they all move in tandem, falling or rising together at the same time, there is no point diversifying. If you drop all your baskets, all your eggs break.

Luckily, different assets possess different characteristics. They behave differently under different market conditions.

In this chapter we will demonstrate what happens when blending a number of assets. We will see that when blended correctly, the risk of the mix is lower and its return pattern is smoother than those of its parts. We will then move to some simple calculations of a portfolio’s expected return and risk.

Typically, there are no free lunches in finance. To get something, you need to either pay or take a risk. But it is said, ‘Diversification is the only free lunch.’ This is because it reduces risk without sacrificing all returns and it does not cost any fees. When offered something for free, take it.

Blending

When imperfectly correlated assets are mixed, the portfolio return is the weighted average of the individual assets’ returns, but portfolio volatility is lower than the weighted average of the individual assets’ volatilities.

Figure 13.1 shows the performance of UK equities, gilts and a blend of 60% UK equities and 40% gilts. This figure empirically reveals the effects of diversification.

The performance of the mix is between those of equities and gilts. Its volatility is lower than that of equities. Blending equities and gilts over this particular time period was exceptionally beneficial. It generated a return in line with the better performing asset (gilts) but with a lower risk than that of equities.

Table 13.1 Annualised return, volatility, Sharpe ratio and max drawdown

	UK equities	Gilts	60/40 mix	40/60 mix
Return pa %	4.9	6.0	5.7	5.9
Volatility pa %	14.2	5.4	8.5	6.1
Sharpe ratio	0.10	0.47	0.26	0.40
Drawdown %	−43.6	−5.9	−21.9	−11.8

Source: Bloomberg. FTSE 100 Index, iBoxx £ Gilts Index, UK Cash LIBOR TR 1 Month Index. January 1998 to December 2015. Based on monthly total returns, measured in £

Table 13.1 shows the return and risk analytics of equities, gilts and 60/40 mix, as well as a 40/60 mix. The 60/40 mix has a return in line with that of gilts, a lower volatility than that of equities, with a superior Sharpe ratio than that of equities.

The volatility of the 60/40 mix is 8.5%. It is lower than the weighted average volatilities of UK equities and gilts of 10.7%.¹

A different mix, such as 40% equities and 60% gilts, gives a different return and risk profile. By changing the blend you can control your portfolio’s return and risk. This is an important observation. We will get back to it later.

Calculating expected return and risk of blended portfolios

The expected return of a portfolio grouping a number of assets is simply the weighted sum of the assets’ expected returns. Put differently, the portfolio’s expected return is the sum of the weight of each asset times its expected return.

For example, assume a portfolio with 60% equities and 40% bonds. Say equities’ expected return is 8% and that of bonds is 5%. The portfolio’s expected return is 6.8%.²

r_p = Σ(w_ir_i)

Portfolio return (r_p equals the sum of (Σ) the weight of each asset i (w_i) times the return of asset i (r_i). Simples.

It is more involved for volatility. In the 1950s, Nobel laureate Harry Markowitz developed Modern Portfolio Theory (MPT). Markowitz showed that the volatility of a portfolio is not simply the weighted average of its assets’ volatilities.

The key for diversification is imperfect correlation (correlation below |plus| 1.0). When two assets are imperfectly correlated, blending them produces a portfolio with volatility lower than the weighted sum of the two assets’ volatilities. The total is less than the sum of the parts.

Calculating portfolio volatility is more complex than calculating expected return.

One definition before we dive into the formula: variance is standard deviation squared (or standard deviation is square root of variance). Whilst standard deviations are not additive, variances are. Now we are ready.

Portfolio variance is calculated by multiplying the squared weights of assets by their corresponding variances. Then adding twice the weighted average variance of each asset pair multiplied by the correlation between each pair.

This is a mouthful of what appears to be gobbledygook. An example can clarify.

In the 60% equity and 40% bond portfolio the standard deviation of equities is 15%, that of bonds is 5% and the correlation between the two assets is 0.20.

Portfolio standard deviation = square root of portfolio variance = square root of 60%² × 15%² + 40%² × 5%² + 2 × 60% × 40% × 15% × 5% × 0.20 = 9.6%.

Another way to look at it is that the formula has two parts. The first part sums the squared weight of each asset times its variance. The second part sums for each different pair of assets, twice their weights, times their standard deviations times the correlation between them.

σ_p² = Σw_i²σ_i² + ΣΣw_iw_jσ_iσ_jρ_ij

Portfolio variance (σ_p²) equals the sum of (Σ) the squared weights of each asset i (w_i²) times its variance (σ_i²) plus for each asset i different from asset j (i ≠ j) the sum of (ΣΣ) the weights of assets i and j (w_i and w_j), times the standard deviations of assets i and j (σ_i and σ_j), times the correlation between them (ρ_ij).

The formula validates that the smaller the correlation between assets, the lower is portfolio volatility, as the formula’s second part is smaller. If correlation is perfectly positive (+1.0), portfolio volatility is the weighted sum of individual assets’ volatilities. With perfect correlation diversification benefits disappear.

The good news is that this is the most complicated mathematical calculation in this book. You now know how to calculate the expected return and volatility of portfolios. What you need is the expected returns, volatilities and correlations of your portfolio’s assets. We will get to it in the next chapter.

What does this mean to you as an investor? Considering investments in portfolio context

When considering each asset’s risk, do not consider it in isolation but in portfolio context. Assess the impact of investing in each asset on your overall portfolio.

For example, say you are risk averse and do not want to invest in equities since they are terrifyingly risky. You hold a portfolio of 100% bonds with 5% volatility.

How does adding a small allocation to equities impact the portfolio?

The volatility of equities is 15% and the correlation between equities and bonds is 0.20. By allocating 5% to equities and 95% to bonds, portfolio volatility is 4.95%.³ Counter-intuitively, adding a risky asset actually reduced portfolio risk thanks to diversification benefits.

The expected return of bonds is 5% and that of equities is 8%. The expected return of the 100% bond portfolio is 5% and that of the 95% bonds and 5% equities is 5.1%.⁴

Adding some equities increased expected return and reduced risk. You improved your portfolio’s Sharpe ratio: higher expected reward for each unit of risk.

Equities in portfolio context in this example are a risk diversifier and return enhancer.

Local versus global diversification

Global diversification is usually beneficial. Equity and bond markets across the globe undergo different economic regimes, leading to imperfectly correlated performance.

Over the last number of decades, the benefits of global diversification have diminished with tighter integration of financial markets, closer cross-border trade relations and greater coordination amongst central banks. Globalisation and technology are two forces bringing markets closer and enhancing information flow. But still, global markets do not move in unionisation.

The Eurozone’s formation, for example, has advanced integration of equity and bond market across Europe. Nevertheless, even within the Eurozone, different markets behave differently.

Take, for instance, the bond and equity markets of Germany versus those of Southern European countries, such as Spain, Italy and, particularly, Greece. Germany and these countries have experienced diverging economic fortunes since the 2008 and 2011 crises, delivering distinctive return and risk profiles. There is still merit for global diversification, even within the union.

As a UK-based investor, consider global diversification. Admittedly, the UK is an open economy, with the majority of companies’ revenues coming from overseas. The local equity market is developed and diversified. Therefore, going global does not make a huge impact. However, at times there is a large divergence between the UK, global developed and emerging equity markets.

Figure 13.2 compares the performance of UK equities, global developed equities, excluding the UK, and emerging market equity (EME). Whilst, during some periods, the performance of UK and global equities is nearly identical, it differs substantially during other times (partially due to currency movements). UK equities and EME can be correlated, but their performance diverges markedly.

When investing globally, do not neglect currency risk. It’s a manageable risk since, in most cases, you can hedge it.

Multi-asset investing

Increasingly, funds follow a multi-asset strategy. These funds blend different asset classes to benefit from diversification; flexibility to dynamically invest across different assets; and harvest a wide range of lowly correlated return sources.

Armed with assumptions about return, risk and correlation of assets, you can combine them into a mix with a targeted return and risk profile or a specific outcome. Hence, some funds are labelled outcome-oriented.

‘Balanced funds’ have, historically, offered old-fashioned multi-asset investing in the UK. These funds often follow an allocation of 60% equities and 40% bonds. However, the overwhelming majority of their risk and return is driven by equities. Equities are more volatile and their expected return is higher than that of bonds. Therefore, over 90% of the ‘balanced’ funds’ risk and return could come from equities – hardly balanced.

A new generation of multi-asset funds is Diversified Growth Funds (DGFs). DGFs are the sexy version of balanced funds. They enjoy more flexibility with their asset mix, some use dynamic asset allocation to enhance returns and mitigate risks and some use sophisticated derivative-based strategies. DGFs are not hedge funds since they are regulated, usually they are more transparent and liquid than hedge funds and, typically, they are not as expensive as hedge funds.

DGFs are active strategies. Their return and risk profile depends on the specific style of their fund managers. When using a DGF, you outsource the asset allocation and investment selection decisions to a professional manager. You can diversify manager risk by blending two to three DGFs – not more, to avoid over complexity and over diversification.

One advantage of DGFs is that they target an outcome matching the needs of most long-term savers. A return of cash + 4% to 5% is appropriate for most phases in the saver’s life.

Concentrated investing

‘Wide diversification is only required when investors do not understand what they are doing.’

Warren Buffett

Remember our basket and eggs. Well, another approach is put all your eggs in one basket and then watch that basket. Just do not drop it.

Diversification reduces some risk, but the return of your portfolio is the average return of its underlying investments. Diversification’s objective is not to make you rich. Rather, it is delivering a smoother return profile and increasing the probability of reaching your objectives, if they are reasonable.

To make a lot of money from investing concentrate, do not diversify. Placing a small number of high-risk bets with high potential reward is the way to generate high returns. This is also a way to suffer large losses when getting it wrong.

Ordinarily, if something appears too good to be true, it is not true. If you identify an investment that seems to be a certain bet – it cannot go wrong – think again. Had it been such a good investment, others would have invested in it, pushing its price upwards, evaporating the opportunity.

I am not saying there are no unique investment opportunities. There are. But be careful and sceptic. Concentration can come not only with high rewards, but also with a high price. You can pay dearly for mistakes.

On the other side of the diversification spectrum sits over-diversification. If you overly diversify your portfolio, by holding a very large number of funds and assets, you might end up holding the entire investment universe – an expensive closet tracker. Diversification should be not too little and not too much.

Three buckets

If you are an expert in a field, having an edge over the market in some area of expertise and you can identify unique investments, by all means invest. Investing in private enterprises, property or exclusive projects can generate higher returns than usually are available in public capital markets. Informational advantage can be turned into profits in the right hands.

But do not forget the principle of diversification. Ensure that whatever happens you secure a minimum standard of living. Never risk what you cannot afford to lose.

Split your assets amongst three buckets. The first is a safe bucket. It holds conservative assets to maintain a minimum standard of living. Use an annuity to secure some income for the rest of your life, keep cash reserve and own your insured home. Minimise volatility and downside risk. Whatever happens, you will have enough on which to live.

A second bucket is a market bucket. It holds long-term savings in a diversified portfolio, invested in capital markets to maintain your current standard of living when retiring. Its objective is your target return. This bucket follows the investment principles we cover in this book.

The third bucket is a speculative bucket. It invests in your area of expertise in a concentrated way. It can hold a private business or buy-to-let properties. This bucket’s objective is to potentially upgrade your standard of living. But, even if losing the third bucket, the other two buckets secure your financial future. Its objective is your desired return. Here, dream big. If you do not aspire to great things, you will not attain small things.

Summary

• Since nobody knows for sure how assets will perform in the future, diversify across different assets.
• The prerequisite for diversification is imperfectly correlated assets.
• By blending assets, you reduce risk and set your portfolio’s expected return and risk profile.
• A portfolio’s expected return is the weighted sum of its individual investments’ returns. Calculate a portfolio’s expected risk using a formula that accounts for individual investments’ volatilities and correlations.
• Consider assets’ risk in portfolio context, not on a standalone basis. What matters is how adding an asset impacts the portfolio’s risk and return.
• Normally, global diversification has rewards. Mind the currency risk.
• Multi-asset investing benefits from diversification across asset classes, as well as from a wide investment opportunity set, the flexibility to dynamically change the asset allocation and the ability to target a desired outcome.
• To generate very high returns, concentrated investing is needed, not diversification. However, concentration comes with risks. Concentrate only when having a high conviction.
• Divide your wealth across safe, market and speculative buckets, which have different roles and potential impact on your wealth.

Notes

¹ 10.7% = 60% × 14.2% + 40% × 5.4%.

² 6.8% = 60% × 8% + 40% × 5%.

³ 4.95% = square root of (95²5%² + 5%² 15%² + 2 × 95% × 5% × 5% × 15% × 0.20).

⁴ 5.1% = 95% × 5% + 5% × 8%.