Asset Allocation in China: Crafting the Optimal Allocation Strategy, Episode II

Author: Randy Cohen, Senior Lecturer of Entrepreneurial Management at Harvard Business School, Member of Advisory Board at Bridge Point Capital


1.3 Diversification within Equities


Focusing on the households that do actually have financial assets invested in equities (either directly or indirectly), a number of authors have also highlighted a second puzzle: the lack of diversification of the equity portfolios. Diversification is the idea, well-established both in the data and in practice, that one can construct portfolios with multiple assets that give an investor more attractive risk-return profiles than what they would get from any particular asset considered alone.


To think coherently about risk and return, we must start by articulating what we mean by ‘risk’ and what we mean by ‘return.’ One measure of return is the average arithmetic return of a given asset or portfolio. One measure of risk – not the only one, but certainly an important one – is the volatility or "standard deviation" of a given asset or portfolio. Exhibit 1 shows these measures for a number of assets, including the US stock market. For investors unfamiliar with standard deviation as a risk measure, it may be helpful to think of it this way: one standard deviation is about what one should expect to lose in a typical bad year; a two standard deviation loss would be a horrible year, and a three standard deviation loss would be the worst year one would expect to see in a century.


Diversification is based on the idea that asset returns are not perfectly correlated with each other, meaning that when we create portfolios of assets we are able to get access to lower-risk ways of delivering the same expected return. Exhibit 3 shows the performance of portfolios constructed from IBM (IBM), Exxon-Mobil (XOM), and Wal-Mart (WMT). The purpose of this example is to demonstrate the power of diversification in delivering attractive risk-return portfolios for investors. It is often said that diversification is the only ‘free lunch’ available in financial markets, in the sense that households can in general easily improve their well-being by selecting diversified portfolios of financial assets.


The data for the following exhibit come from the last six years of daily trading for each stock. The mean daily return for IBM over that period has been 0.0186 percent, with a daily volatility of 1.195 percent. This gives an (annualized) Sharpe Ratio – a measure of the return, scaled by risk – of 0.247. The Sharpe ratio of XOM is 0.317, and WMT is 0.356. But look at what happens when we put together an equally-weighted portfolio of the three stocks – the Sharpe ratio (the measure of return, scaled by risk), rises to 0.387, which is not only higher than the average of the three stocks, it is higher than the highest of the three. Diversification is the easiest way to improve a household’s expected return without taking on additional risk.


Exhibit 3 – Ibm, Exxon/Mobila and Wal-Mart Diversification Example

A graphical interpretation of the risk-return tradeoff and the power of diversification can be helpful. Exhibit 4 shows a hypothetical scenario where a number of assets exist, each with their own risk and return. Each asset or portfolio is represented by a point in space – households would prefer more return for any given amount of risk, or less risk for any given amount of return. If this exhibit could be thought of as a map, investors would always want to travel towards the northwest, towards higher return for lower risk. In this exhibit the assets could be individual stocks, asset classes, or any other potential investment whose risk and expected return can be estimated.


Exhibit 4 – General Diversification

Exhibit 5 shows how portfolios can be constructed that have better risk/return profiles than the individual assets alone. The set of ‘best’ portfolios – portfolios that give that lowest risk available for a given level of return – forms a ‘frontier,’ or a curved line, in the graph; this is the famous "efficient frontier" of optimal portfolios.


Exhibit 5 – Efficient Frontier

If there is, in addition to risk assets, a risk-free asset available, that further improves the options available to investors -- they can move further "north" and "west."


Exhibit 6 – With Risk-Free Asset

The upshot of this is that households, if they are behaving optimally, should always choose diversified portfolios of assets. But, as highlighted by Goetzmann and Kumar (2008), households that invest in equities often have portfolios that are highly concentrated into a handful of stocks. Goetzmann and Kumar did research into the actual portfolios of a sample of households that invested in stocks through a discount brokerage. In the Goetzmann-Kumar sample, the average number of stocks held by households ranged from four to seven, well short of the numbers recommended based on optimizing risk-return tradeoffs. Investing in this way means that investors are foregoing the opportunity to enhance their risk/return tradeoff through diversification. It can be hard for investors to invest directly in a large basket of stocks themselves, which is another reason the advent of mutual funds and ETFs has done so much to improve investor welfare.


One other note: not only do investors invest in a small number of stocks, they tend to invest heavily in the company they work for. Benartzi et al (2007) focus on this puzzle, and highlight the fact that investing in own-company stock represents a poor approach to managing the various risks that households face. In particular, investing in own-company stock ties the performance of the household’s financial assets to the performance of its human capital. Benartzi et al estimate that the value of own-company stock in a retirement portfolio is as little at 50 cents on the dollar of nominal wealth. (See also Benartzi and Thaler (2007) and Muelbroek (2002)).

1.4 International diversification


One of the biggest puzzles in investing is the "home bias" -- the tendency of investors to invest primarily or even solely in their home country, thus missing out on the benefits of international diversification. Just as going from one stock to three (or more) improves the risk-return tradeoff, going from one country to three (or more) can hugely benefit investors in exactly the same way. A large literature investigates the home bias puzzle (e.g. French and Poterba, 1991). The general thrust of this literature is that investors should have at least some assets invested in international (from their perspective) assets, due to the improvement in risk-return tradeoff that this allows. The welfare cost of restricting holdings to only domestic assets depends on a number of factors, but in particular the size of the domestic market relative to the size of the world market and the degree to which internal and external markets are correlated. Home bias in a large equity market like the United States has less of a welfare cost than home bias in a smaller equity market such as Belgium (with China falling somewhere in between). We will see in Section 4 that the expected benefits to Chinese investors of international diversification are extremely large.


1.5 Alternative assets


In recent years we have seen enormous growth in so-called "investable alternative" assets. The three main alternative categories are hedge funds (also known as "absolute return), private equity, and investable real estate. Absolute return strategies can enormously benefit investors' portfolios due to their low correlation with other markets -- these investments have their ups and downs, but if they come at different times than the ups and downs of stock and bond markets they can still moderate risk. Private equity and real estate have significant correlation to equity markets, but through their use of long-term leverage these asset classes have the potential to offer high long-run returns. Including alternative investments can create additional diversification in a portfolio, thus reducing risk. Whenever risk is reduced, investors can convert the risk benefit to a return benefit by reducing the allocation to cash. In Section 2 we will observe the substantial role that alternatives can play in a "best practices" portfolio.

1.6 Investing Across the Life Cycle


Most experts feel that investors should hold riskier, higher-expected-return portfolios in their prime earning years and safer portfolios when they are in or near retirement. Research in the 1960s spelled out special conditions under which household portfolio shares should be age-invariant (Merton 1969), but the general professional and academic consensus is that these conditions do not hold in practice. Empirically, the evidence that households actually follow the standard advice has been limited (Ameriks and Zeldes (2004)), although there is some evidence of a shift out of risky assets precisely at the time of retirement. So we can add one more to our list of puzzles -- investors do not appear to optimally adjust their portfolios as they move through the life cycle.


1.7 The Role of Robo-Advisors


Good financial advice requires helping investors overcome the constraints and biases that lead to the puzzles above. This means having a strong understanding of the expected returns and risks of different asset classes, including subtle risks involving correlations. It requires complex optimization calculations. And it requires recognizing and accounting for investors' differing needs across the stages of their lives. Historically, such advice has been very costly, and consequently few investors have availed themselves of it. Thus we see many, indeed most, investors missing out on opportunities to improve their investment portfolios.

However, recent technological innovations have made helpful advice available at surprisingly low cost. The new source of information is commonly known as a "robo-advisor."


Robo-advisers are computer software programs in which crucial information about investors, their current holdings and investment goals are inputs. The software then delivers to the investor advice on what changes to make to the portfolio in order to move toward optimality. A key advantage of robo-advisors is their low cost. Additionally, they are available around the clock. And they are not subject to human behavioral biases, which can be an important advantage.


There are also some disadvantages. For example, a robo-advisor can only take into account information it was programmed to, and can fail to appreciate subtlety and nuance. Needs and wants that are conveyed only through tone of voice or other means of communication will be difficult or impossible for a robo-advisor to pick up on. Robo-advisors offer only advice, whereas a human advisor can do much more. A human advisor can be a teacher, and can also offer psychological benefits akin to a coach or personal trainer -- having a real, live financial advisor may mean that the investor feels accountable to someone in their savings decision, which may lead them to save more. With robo-advisors there may not be this accountability effect.


Here are some things we can say with confidence about the future of robo-advising. First, robo-advisors are going to get better and better every year. Any critique anyone makes of robo-advisers will be less true in a year and probably not true at all in five or ten years, as robo-advisors continue to advance in sophistication, as well as in the amount of information they're able to take account of. Second, while at this moment, human advice is superior to Robo advice, we have almost certainly reached the point where the human/robo advisor combination is superior to human alone. And indeed the very best human advisors will be the ones who are the most skillfully able to understand what the software does and to add value on top of it, as opposed to replacing it. Third, we will probably never reach the point where robo advice alone is superior to human-plus-robo advice. Fourth, we have reached the point where for many millions of people who find human advisors too costly, robo advice is already the best value for them. We conclude that even today robo advice adds value for two important groups – lower wealth investors who can now get good advice instead of no advice, and higher wealth investors who can now get advice through the combination of human and robo advisor.