The right investment portfolio for you is the one that achieves your financial goals with the minimum of risk. This sounds good but what does it mean in practice? For example, how can we compare two different investment options where one has a higher return but also a higher risk?
The first step is to understand your financial goals. To illustrate, you may need to save $1 million to retire and you must decide an appropriate allocation to stocks and bonds. Stocks have higher average returns than bonds but are riskier. Risk in this context means two things:
- The ups and downs of the value of your investments along the way. If you can’t tolerate the price volatility, then you might abandon the plan before you achieve your goals. To avoid this, we can use the historical record of markets as an indicator that the proposed portfolio is unlikely to exceed your personal tolerance to this type of risk. Quantifying your personal risk tolerance is far from an exact science but helps set an upper limit to the risk exposure.
- Some portfolios may be eliminated as too conservative to reach your $1 million target given reasonable assumptions about your retirement date, savings rate and other factors that are part of financial planning.
- Within these upper and lower bounds there often remains a range of portfolio choices. We can look at historical data to understand the tradeoffs between different options. Table 1 shows the 20-year performance of a range of historical well diversified index portfolios[1].
Table 1
| | Equity Allocation (%) |
| | 0 | 40 | 60 | 80 | 100 |
| Return | 3.63% | 5.70% | 6.68% | 7.61% | 8.48% |
| Volatility | 3.96% | 5.69% | 7.45% | 9.40% | 11.44% |
| Average Value of $100 after 20 years (A) | $204 | $303 | $364 | $434 | $509 |
| Average Value of $100 after 50 years (B) | $595 | $1,599 | $2,536 | $3,914 | $5,854 |
| | | | | | |
| Risk adjusted measures | | | | | |
| Sharpe ratio | 0.41 | 0.65 | 0.63 | 0.60 | 0.57 |
| Risk adjusted end wealth ratio after 20 years (C) | 0.93 | 0.90 | 0.87 | 0.83 | 0.80 |
| Risk adjusted end wealth ratio after 50 years (D) | 0.89 | 0.84 | 0.79 | 0.74 | 0.69 |
Source: Author calculations
The return and volatility are shown for a range of asset allocations from 0-100% equity, with the balance in bonds. We also show the cumulative value of $100 invested for 20 years and 50 years, assuming the same return every year. For example, a 60% equity, 40% bond portfolio has an average annual return of 6.68%, a volatility of 7.45% and the average value of an initial investment of $100 after 20 years is $364 and $2,536 after 50 years. 50 years may seem a long time but is the period of a 30-year-old investing until they are age 80.
As expected, the portfolio with a 100% allocation to stocks has the highest return. This might not be our preference because it also has the highest volatility. Is the extra return worth the extra pain (as measured by volatility)? To help answer this question, we calculate the ratio of return to risk, which is one way of measuring the risk-adjusted return. We deduct the risk-free return (the return from a cash savings account, assumed to be 2%) from the portfolio returns so the ratio indicates the additional value from investing in cash. This ratio is called the Sharpe ratio and is listed in the table. A higher Sharpe ratio indicates a higher return per unit of volatility. From the table, the maximum Sharpe ratio is at 20% equity. The Sharpe ratio declines as the equity allocation increases implying that additional equity exposure yields a diminishing increase in return.
We may also be interested in the risk of falling short of our investment goals. We know that a higher equity allocation, on average, leads to higher growth but how does the higher portfolio volatility impact the risk of falling short of desired end goal? Suppose our retiree wanted to have $1million in her retirement account but achieved only $700,000? By analogy with the Sharpe ratio, we focus on the shortfall risk of ending up with less wealth than if we had invested in the risk-free asset (cash). In this case the risk penalty is calculated as the cost of insuring against this possibility as described in our previous blog on risk. The insurance cost is deducted from the initial capital and the cost of insurance grows as the allocation to equities increases. For ease of comparison, we show (Table 1) the risk-adjusted end wealth divided by the average end wealth (A&B) as the risk adjusted end wealth ratio (C&D).
For the 60% equity, 40% bond portfolio the risk adjusted end wealth ratio after 20 years is 0.87 and 0.79 after 50 years. We observe:
- Increasing equity allocation is less effective at reducing the risk of shortfall as the equity allocation increases.
- As the investment horizon increases, the risk of shortfall increases.
The last point may come as a surprise. It is tempting to assume a constant average annualized return which compounds over time. We don’t know the specific future sequence of investment returns that are in store for us, but we do know that the outcome is not going to be average. Due to the inherent risk of markets some of these paths lead to a shortfall. Periodic re-evaluation of your portfolio choice is key to keeping your financial goals on track. The author recently bought a battery electric vehicle (BEV). It is capable of remarkable acceleration which offers both the potential of getting to a destination faster and taking longer (speeding tickets and accidents). And so it is with investing, increasing your equity allocation may provide excitement without achieving your destination more reliably.