Not all index and passively managed funds are created equal. Even two passively managed funds within the same asset class (such as U.S. small value) can have very different portfolio construction rules that lead to different loadings on factors, and different expected returns.
The role of REITs in a diversified portfolio.
The importance of knowing when you have “enough.”
Recommended investment vehicles.
Appendix A: Monte Carlo Simulations
In “traditional” retirement planning, annual investment returns are assumed to be a constant number, such as 6 percent per year. Retirement planners arrive at this number based on a portfolio’s asset allocation and on assumptions about the returns of various investments. Outcomes using this computation typically are presented as expected wealth values over the anticipated period of retirement.
The problem with this approach is that investment returns are not deterministic. While investing is about risk, retirement calculators that present single scenarios treat outcomes either as a certainty or, at best, a 50/50 proposition (for instance, the odds are 50/50 that you will do better or worse than the expected result). Investing is not a science in the same way physics is. No one knows with precision, beforehand, what the return of different investments will be over any given number of years. Investment returns are random variables, characterized by expected values (averages), standard deviations and, more generally, probability distributions. For this reason, projections of an investment program’s possible results should also be expressed in terms of probabilities. For example, an expected outcome should be presented in terms such as:
There is a 95 percent chance you will not run out of money in retirement.
There is a 50 percent probability you will accumulate at least $3.1 million.
There is a 25 percent chance you will accumulate $5.2 million or more. But, there is also a 10 percent chance you will accumulate only $400,000 or less.
To arrive at this type of conclusion, it is necessary to use a tool known as a Monte Carlo (MC) simulation.
MC simulations require a set of assumptions regarding time horizon, initial investment, asset allocation, withdrawals, savings, retirement income, rate of inflation, correlation among different asset classes and—very importantly—the return distributions of the portfolio.
In MC simulation programs, the growth of an investment portfolio is determined by two important inputs: portfolio average expected return and portfolio volatility, represented by the standard deviation measure. Based on these two inputs, the MC simulation program generates a sequence of random returns from which one return is applied in each incremental period (typically one year) of the simulation. This process is repeated thousands of times to calculate the likelihood of possible outcomes and their potential distributions.
MC simulations also provide another important benefit: They allow investors to view the outcomes of various strategies and how marginal adjustments in asset allocation change the odds of these outcomes. We will examine the results for a hypothetical investor who begins with a $1 million portfolio. An initial withdrawal is made equal to the specified withdrawal rate multiplied by the $1 million starting value. The remaining assets then grow or shrink per the asset returns in the replication for that year. At the end of the year, the portfolio is rebalanced back to investor’s target allocation. In subsequent years, the withdrawal is the prior year’s withdrawal plus inflation for that year. Withdrawals are made at the start of each year. It is assumed that taxes are included in the withdrawal amount.
The following table shows the real return capital market assumptions used in the MC simulation. It is important to note that the results from any MC simulation will be based on its inputs. If we were to use different capital market assumptions, the results in the tables that follow would be very different. We build capital market assumptions using current valuations and yields, so these assumptions will change over time.
Capital Market Assumptions
This section will look at portfolios with various hypothetical allocations. The success rate is defined as the probability that the portfolio has at least one dollar at the end of the planning horizon. Of course, if someone has a 95 percent success rate, this also means that investor has a 5 percent chance of failure. Outcomes are calculated over a 30-year horizon. We will review the results using three different initial withdrawal rates: 3 percent, 4 percent and 5 percent. A 4 percent withdrawal rate on a $1 million starting portfolio indicates that $40,000 is withdrawn in the first year, and then adjusted for inflation thereafter.
Portfolio A: 60 percent total stock market/40 percent fixed income
Portfolio B: 60 percent equity tilted to small-cap and value/40 percent fixed income
Portfolio C: 40 percent equity tilted to small-cap and value/60 percent fixed income
The equity portion of the portfolios tilted to small-cap and value stocks have loadings of 0.5 on the size factor and 0.2 on the value factor.
Odds of Success (%)
At a relatively low 3 percent withdrawal rate, changes in asset allocation do not have a significant effect on success rates. However, by making such a change, an investor could slightly improve the odds of success while reducing the portfolio’s equity allocation. At a 4 percent withdrawal rate, we see significant improvement in success rates by tilting the equity portion of the portfolio to small-cap and value stocks. At a relatively high 5 percent withdrawal rate, no amount of changes in the asset allocation will get the investor to an acceptable success rate. This investor should reduce their spending, plan on working longer, lower their goal or find other sources of income.
We will now examine how adding the alternative investments we have discussed to Portfolio B (60 percent equity tilted to small-cap and value stocks/40 percent fixed income) affect the odds of success.
Impact of Adding Alternatives
We will replace 15 percent of Portfolio B’s 60 percent equity allocation with alternatives (Portfolio B1). We will use a naïve 1/N allocation. Thus, our five alternatives, the AQR Style Premia Alternative Fund (QSPRX), the AQR Managed Futures High Volatility Fund (QMHRX), the Stone Ridge Alternative Lending Risk Premium Interval Fund (LENDX), the Stone Ridge Reinsurance Risk Premium Interval Fund (SRRIX) and the Stone Ridge All Asset Variance Risk Premium Interval Fund (AVRPX), each receive 3 percent. We will also replace 25 percent of Portfolio B’s 60 percent equity allocation with alternatives (Portfolio B2). This 25 percent allocation is split equally among the same funds that are in Portfolio B1, each receiving 5 percent. It is important to note that these allocations are simply for illustrative purposes (though they are consistent with our belief in efficient markets and that all risky assets should have similar expected returns). Changing the weights within the alternatives allocation or changing their mix does not significantly change the results. We also would see similar results if we pulled the allocation to alternatives from fixed income instead of from equities. The biggest driver of the change in success rates is the size of the alternatives allocation, not which strategies are selected for inclusion in that part of the portfolio.
Odds of Success (%)
At the 3 percent withdrawal rate, we again see relatively small (but positive) changes in success rates. At a 4 percent withdrawal rate, we see meaningful improvements in success rates. At a 5 percent withdrawal rate, we again fail to see much improvement in success rates. The likely reason for this last outcome is that a 5 percent withdrawal rate is not sustainable (at least at today’s fixed income yields and equity valuations).
The combination of tilting the equity portfolio and adding alternatives significantly improves MC simulation success rates. Compared to our starting point, the market-like Portfolio A, Portfolio B1, with a 15 percent allocation to alternatives, improved the odds of success with 3 percent, 4 percent and 5 percent withdrawal rates by 6 percentage points (from 93 percent to 99 percent), 17 percentage points (from 70 percent to 87 percent) and 21 percentage points (fr
om 40 percent to 61 percent), respectively. Let’s consider another way to think about this. At a 4 percent withdrawal rate, Portfolio A had a success rate of just 70 percent. Those odds might be unacceptable, forcing you down to the lower 3 percent withdrawal rate. Adding the 15 percent allocation to alternatives improves the odds of success at the higher 4 percent withdrawal rate to 87 percent. If 87 percent was an acceptable success rate to you (if you would still have options you could exercise if left tail risk appeared), you could then increase your withdrawals from 3 percent back to 4 percent, a 33 percent increase in spending over your retirement. Portfolio B2, with a 25 percent allocation to alternatives, improves the odds of success even further (all the way to 92 percent at a 4 percent withdrawal rate).
Adding unique sources of risk that provide an equity-like return changes a portfolio’s potential distribution of returns in a favorable way. You can use this knowledge not only to improve the odds of achieving your financial goals, but also to increase your spending during retirement.
Appendix B: Other Known Sources of Return
Momentum
A cross-sectional momentum-based strategy buys stocks that have done relatively well over the past 12 months and shorts stocks that have had relatively poor returns over the same period. Narasimhan Jegadeesh and Sheridan Titman, in their 1993 paper, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency,” which appeared in The Journal of Finance, are generally credited in academia for discovering momentum. In this paper, the authors found that recent relative winners (over the previous three to 12 months) will continue to be relative winners over the next three to 12 months, and recent relative losers will continue to be relative losers over the next three to 12 months. They found the effect disappears after 12 months.
In 1994, Cliff Asness, as part of his Ph.D. dissertation titled “Variables that Explain Stock Returns,” found long-term winners eventually become growth stocks that underperform and long-term losers eventually become value stocks that outperform. His was one of the first papers that argued value and momentum are related.
In 1996, Eugene Fama and Kenneth French compared all the market anomalies known at the time to their Fama-French three-factor model. They found momentum was the only anomaly to survive and not be captured by the size and value effects.
In 1997, Asness further explored the relationship between value and momentum strategies in a paper published in the CFA Institute’s Financial Analysts Journal. He found that value tends to be strongest among low-momentum stocks and weakest among high-momentum stocks. He also found that momentum strategies work across the value-versus-growth spectrum.
Also in 1997, Mark Carhart augmented the Fama-French three-factor model with a fourth factor based on momentum. The new momentum factor made a valuable contribution to the explanatory power of the model. In addition, he found that momentum stocks are correlated with each other.
The most commonly cited concern regarding momentum strategies centers around transaction costs. A momentum strategy creates high turnover. This raises the question of whether the momentum premium survives in the “real world” with real trading costs. The 2012 paper “Trading Costs of Asset Pricing Anomalies,” authored by Andrea Frazzini, Ronen Israel and Tobias Moskowitz, found that actual trading costs are low enough to allow the momentum premium to survive.
From 1927 through 2016, the average annual cross-sectional momentum premium was 9.3 percent.
Profitability
A June 2012 study by Robert Novy-Marx, “The Other Side of Value: The Gross Profitability Premium,” offered new insights into the cross-section of stocks returns. His data sample covered the period from 1962 through 2010, and employed accounting data for a given fiscal year starting at the end of June of the following calendar year. The following is a summary of Novy-Marx’s findings, which have affected the way many value investors (such as Dimensional Fund Advisors) construct portfolios:Profitability, as measured by gross profits-to-assets, has roughly the same power as book-to-market ratio (a value measure) in predicting the cross-section of average returns.
Profitable firms generate significantly higher returns than unprofitable firms, despite having significantly higher valuation ratios (that is, higher price-to-book ratios).
Profitable firms tend to be growth firms (profitable firms grow faster). Gross profitability is a powerful predictor of future growth in earnings, free cash flow and payouts.
The most profitable firms earn a 0.31 percent per month higher average return than the least profitable firms. The data is statistically significant (with a t-statistic of 2.49).
Controlling for profitability dramatically increases the performance of value strategies, especially among the largest, most liquid stocks. Controlling for book-to-market ratio improves the performance of profitability strategies.
Because both gross profits-to-assets and book-to-market ratios are highly persistent, the strategies’ turnover is relatively low.
Because strategies based on profitability are growth strategies, they provide an excellent hedge for value strategies. Adding profitability on top of a value strategy reduces overall volatility because the two strategies are negatively correlated.
As additional evidence that the two strategies combine well, consider the following: While both profitability and value strategies generally performed well over the study’s sample period, both had significant periods in which they lost money. Profitability performed poorly from the mid-1970s to the early 1980s and over the mid-2000s while value performed poorly in the 1990s. However, profitability generally performed well during the periods in which value performed poorly and vice versa. As a result, the mixed profitability/value strategy never experienced a losing five-year period.
In summary, the research has found profitability to be persistent over long periods, pervasive around the globe, robust to various definitions and implementable. From 1964 through 2015, the average annual profitability premium was 3.0 percent.
Quality
Building on Novy-Marx’s work, researchers have since extended the profitability factor to a broader quality factor (the returns to high-quality companies minus the returns to low-quality companies) that captures a larger set of quality characteristics. While there is no one consistent definition of quality, in general, high-quality companies have the following traits: low earnings volatility, high margins, high asset turnover (indicating the efficient use of assets), low financial leverage, low operating leverage (indicating a strong balance sheet and low macroeconomic risk) and low specific-stock risk (volatility unexplained by macroeconomic activity). Companies with these characteristics historically have provided higher returns, especially in down markets. In particular, high-quality stocks that are profitable, stable, growing and have a high payout ratio outperform low-quality stocks with the opposite characteristics.
Jean-Philippe Bouchaud, Stefano Ciliberti, Augustin Landier, Guillaume Simon and David Thesmar, authors of the study “The Excess Returns of ‘Quality’ Stocks: A Behavioral Anomaly,” which was published in the June 2016 issue of the Journal of Investment Strategies, examined the quality factor and found that its performance in the United States for the period from 1990 through 2012 was very strong, producing a Sharpe ratio of 1.2 with a highly significant t-stat of about 6. It was also highly successful in all geographical areas.
From 1958 through 2015, the average annual quality premium was 4.0 percent.
Carry
The carry factor is the tendency for higher-yielding assets to provide higher returns than lower-yielding assets. It is a cousin to the value factor, which, as you recall, is the tendency for relatively cheap assets to outperform relatively expensive ones. A simplified description of the carry trade is the return an investor receives (net of financing) if asset prices remain the same. The classic application is in currencies (going long the currencies of countries with the highest interest rates and short the currencies of those with the lowest). Currency carry has been both
a well-known and productive strategy over several decades. However, the carry trade is a general phenomenon.
Ralph Koijen, Tobias Moskowitz, Lasse Pedersen and Evert Vrugt, authors of the 2015 study “Carry,” write: “While the concept of ‘carry’ has been applied almost exclusively to currencies, it … can be applied to any asset.” They defined carry as the expected return on an asset assuming its price does not change—that is, stock prices do not change, currency yields do not change, bond yields do not change and spot commodity prices remain unchanged. Thus, for equities, the carry trade is defined by the dividend yield (the strategy involves going long countries with high dividend yield and short countries with low dividend yield). For bonds, it is determined by the term structure of rates. For commodities, it is determined by the roll return (the difference between spot rates and future rates).
The authors found a carry trade that goes long high-carry assets and shorts low-carry assets earns significant returns in each asset class they examined with an annualized Sharpe ratio of 0.7 on average. Further, a diversified portfolio of carry strategies across all asset classes (stocks, bonds, commodities and currencies) earns a Sharpe ratio of 1.2. They also found that carry predicts future returns in every asset class with a positive coefficient, but the magnitude of the predictive coefficient differs across asset classes.
Reducing the Risk of Black Swans Page 11