Roboadvisors (part 1) : we'll be back...
According to the financial times two factors explains why only a small proportion of investors choose to change their Wealth Manager :
- Wealth managers can make it difficult for consumers to break up with them, by charging high exit fees.
- People usually don't like to take big decisions, especially when their level of knowledge and experience is low, which is often the case with financial topics.
The fact that investors are reluctant to change their advisor may also explains why robo-advisors are slow to gain ground with investors. This will eventually change, as exit penalties are less and less tolerated by financial regulatory authorities and as younger generations are more and more prone to use those kind of services : 11% of the investors born between the mid 1960s and early 1980s are already using robo-advisors, one way or another.
But what are exactly robo-advisors ? What are they able to do ? Are they a real alternative to human advisors ? What are their limits ? In this series of articles we will try to find responses to some of those questions and have a better understanding of their strengths and weakness.
We will start by describing a typical process used to construct an investor portfolio in the wealth management industry. With this knowledge in mind, we will try to understand what may be automated in the process and how the latest evolution in technology (like kafka streams, kafka connect and debezium) can help us to do it.
Construction of an investor portfolio is a three step process. First, the investor has to decide how to allocate his money among different assets categories, such as equities and fixed-income. Second, he has to decide how much to invest in this risky portfolio versus in a risk free asset, such as short time bills or money market funds. Finally, he has to pick the best assets to include in each category of the risky portfolio.
Portfolio optimization and stock picking require solid statistical and functional knowledge and experience. But deciding what portion of an investor's capital to invest in the risk free asset and what portion to invest in the risky portfolio is much more simpler and depends more on the investor appetite for risk. So let's start there.
Capital allocation to risky asset
The investor has to decide how much risk he is willing to take, versus how much return he expects. To be able to compare different risky portfolios on a common ground, an investor needs to scale each portfolio's expected return for the level of risk it represents. In 1966, an American economist, William F. Sharpe has created a tool, the reward to volatility ratio - or Sharpe ratio - to measure what additional amount of return an investor receives per unit of increase in risk.
This equation subtracts the return of the risk free asset (Rf, available at no risk) from the expected return of the risky asset (E[ra]), before dividing the result by the risky asset standard deviation (σa ), which is is used as a measure of risk. By choosing the portfolio with the biggest Sharpe ratio, the investor is sure to invest in the portfolio with the largest expected reward for the risk he is taking.
Let's take an example. The investor has to choose between a portfolio A, with an expected return of 4% (Ra) and a standard deviation, of 7% (σa) and a portfolio B with an expected return of 5% (Rb) and a standard deviation, of 10% (σb). We'll assume the risk-free rate Rf is 1%.
- The reward-to-volatility ratio of the portfolio A is (4%-1)/7% = 0.429%
- The reward-to-volatility ratio of the portfolio B is (5%-1)/10% = 0.4%
When both portfolio's returns are scaled for risk, the portfolio A seems more interesting, which is not the case by looking only at their returns.
The Sharpe ratio will also allow the investor to draw the capital allocation line (figure 2). This graph represents all the possible risk-return combination of a two asset portfolio containing a risk-free asset and the risky portfolio.
The x-intercept is the risk-free rate and the slope of the line is the reward-to-volatility ratio (S in the figure 1).The line represents the expected return at each level of risk.
The first element to understand is that a portfolio with a bigger Sharpe ratio, and thus a bigger slope, will be preferable as for any given level of risk, the expected revenue will be higher.
The second point critical to understand is that, by increasing the weight of the risky asset (and decreasing the weight of the risk-free asset) we move from left to right on the capital allocation line. Conversely, by decreasing the weight of the risky asset (and increasing the weight of the risk-free asset) we move from right to left. By changing the proportion he wants to invest in each of the two assets an investor is able to position his portfolio at the right level of risk-return. If for any reason, he decides to increase it's expected return (and to take more risk), he his able to do it very easily by increasing the weight of the risky asset and moving up the slope, without changing the proportion of the assets in his risky portfolio. Moreover, if the expected return or the volatility of the risky portfolio changes during it's investment horizon, the investor is able to keep his level of risk-return stable by maintaining the proportion between both assets
Risk aversion and utility function
Not all investor have the same willingness (and the same capacity) to take risks. Some, like Bodhi Salver in figure 3, are willing to take risk : they are called risk lover. They may engage in what is called a "fair game" (a risk without a risk premium) for the pleasure to confront risk.
Some other are risk-neutral, they take their decisions based solely on the expected risk return ratio. They are not afraid to take risks as long as the expected return is proportional.
Finally, some investors are risk-averse, which mean that they "penalize" the expected rate of return of an investment because of the risk it implies. The bigger the risk, the bigger the penalty.
Because of those differences in risk perception a given point on the capital allocation line may be seen as an opportunity for a risk averse investor, but as a show stopper for a risk lover (and vice versa). That's why the investor needs to use an utility function (like the one in figure 4) that accounts for the risk aversion factor.
The utility function in figure 4 let the investor assign a utility score to a portfolio, by taking it's expected return E(r) and subtracting half of it's variance multiplied by A, which is the risk index of the investor's risk aversion. Based on this, given an investor risk index, it is now possible to draw the indifference curve, which connects all the portfolio with the same utility value.
One element to remember is that, given the choice, an investor will always choose the highest indifference curve as portfolios on higher indifference curves offer higher expected return for a given level of risk.
By replacing the expected return and the variance in the utility function by the weighted expected return and weighted variance (figure 6) and maximizing for y, the investor will produce the optimal weight in the risky portfolio (figure 7)
This weight represents the portfolio with the allocation (risky asset - risk free asset) where the highest possible indifference curve is tangent to the CAL (figure 8)
Let's take an example. The optimal weight for a portfolio with the following characteristics [Rf = 1%, Ra = 4%, σa = 22%], given an investor with a coefficient of risk aversion A = 4 is :
y= (0.04-0.01) / (4 * 0.222) = 0.155 or 15.5%
In this example, this particular investor should invest 15.5% of his capital in the risky asset and 84.5% in the risk free asset. With 15.5% invested in the risky asset, the expected return and standard deviation of the complete portfolio is :
E(Rp) = 0.01 + [0.155 * (0.04-0.01)] = 0.01465 or 1.465%
σp = 0.155 * 0.22 = 0.0341 or 3.41%
Et voilà ! Next time, we will talk about the differences between active and passive strategies. We will also study the concept of efficient frontier that will help us to optimize our risky portfolio.
