The traditional Markowitz mean variance optimization

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1 Evaluating New Methodologies in Asset and Risk Allocation Thomas M. Idzorek, CFA President Morningstar Investment Management Chicago Risk parity strategies favor bonds over equities, but they do not necessarily outperform a static portfolio of 60% equity/40% bonds. Portfolio optimization is evolving beyond traditional Markowitz mean variance optimization to incorporate the higher moments of skewness and kurtosis, which are applicable to alternative investments. The traditional Markowitz mean variance optimization (MVO) paradigm has been popular and served the industry well, but it is time to embrace expanded versions of the framework to take into account the current investing environment. Risk parity and risk-factor-based asset allocation have received a lot of attention, but neither offers a magic result. I will discuss some marketing-oriented materials that act as practitioner-oriented papers, and I will be particularly critical of risk parity. I will touch on the modern investment management process that I think encompasses the generally agreedon best practices of constructing and implementing an asset allocation. I will discuss a number of different asset allocation frameworks, beginning with Harry Markowitz s MVO paradigm, which I call Markowitz 1.0. Then, I will explore risk parity and asset allocation based on risk factors as opposed to asset classes. Next, I will discuss liability-relative optimization, followed by a discussion of what I call Markowitz 2.0. Finally, I will explore the future development of portfolio construction, an area in which practitioners do not spend enough time, and the incorporation of nonnormal distribution assumptions into the optimization process. Modern Investment Management The modern investment management process, whether based on risk factors or asset classes, ultimately requires capital market assumptions, which include the following: 1. expected returns of those asset classes or risk factors, This presentation comes from the Asset and Risk Allocation Conference held in New York City on April 2013 in partnership with the New York Society of Security Analysts. 2. expected variation in returns, and 3. an expected correlation matrix of all asset class pairs. These three inputs are fed into an optimizer, which traditionally has been based on Harry Markowitz s MVO framework, resulting in an efficient frontier. Next, the resulting efficient mix of asset classes or risk factors forms the policy portfolio that needs to be implemented. This can be done with all passive options, all active, or some combination of the two. Most investors hire managers to implement different sleeves or pie pieces from the policy portfolio. Active managers are typically not style-pure and thus have exposure to one or more asset classes or risk factors. We like to think of active managers as a collection of beta exposures or asset class exposures plus a residual return that is not explained by the other exposures. That residual or alpha, as the industry calls it can be positive or negative. In his famous article The Arithmetic of Active Management, William F. Sharpe (1991) explains how alpha is a zero-sum game prior to fees and a loser s game after fees. A Review of Markowitz 1.0. Nobel laureate Harry Markowitz formally invented the concept of mean variance optimization in the 1950s in his landmark work Portfolio Selection: Efficient Diversification of Investments (1959). The inputs of his MVO framework, which he introduced in this book, are expected returns, expected standard deviations, and expected correlation coefficients. These inputs go into the black box of an MVO optimizer, and the output is an optimal weight for each asset class or risk factor along an efficient frontier. Each point along the efficient frontier represents a combination of those asset classes (or asset risk factors) that maximize expected return per unit of risk, expressed as 2013 CFA Institute cfapubs.org December

2 CFA Institute Conference Proceedings Quarterly variance, or standard deviation. The asset class with the highest amount of risk does not necessarily have the highest amount of expected return. Coupling Markowitz s MVO framework with Sharpe s work on the capital asset pricing model (CAPM) produces what most people consider to be the crux of modern portfolio theory. In the classical representation, a capital market line (CML) connects the risk-free rate of return with the point of tangency on the efficient frontier. According to the CAPM, this point of tangency should be the allinclusive global market portfolio. I believe that the Markowitz paradigm is widely recognized as the gold standard or textbook approach to connecting beliefs and expectations about risk/return with the determination of an optimal portfolio. But practitioners are now questioning Markowitz s MVO paradigm. Surveying the literature, there are several criticisms (with some potential solutions) of the Markowitz paradigm. First, the Markowitz paradigm is theoretically a single-period framework. It can be applied over a day, a week, a month, a year, or 20 years. Most people are coming up with annual capital market assumptions, deriving an efficient frontier based on the annual assumptions and then often using the arrivedat policy portfolio for 10- or 20-year time periods. Second, when used with typical capital market assumptions, the Markowitz framework does not result in diversified asset allocations but, rather, concentrated exposures to a few asset classes. In addition, traditional MVO portfolios have unstable asset class weights over time. Both of these welldocumented problems stem from the difficulty of forecasting expected returns and the sensitivity of the MVO to even miniscule changes in returns. There are several common practitioneroriented solutions to highly concentrated portfolios. The most common is to set explicit constraints when running an optimization. Another potential solution is to use one of the types of resampling in which a multivariate Monte Carlo simulation is used to generate thousands of permutations of the capital market assumptions; each permutation is used to generate a new efficient frontier, and the resulting asset allocations from the thousands of efficient frontiers are averaged in some fashion. Different providers of resampled optimization software apply slightly different approaches. The third solution is the Black Litterman model, which starts by reverse-engineering the expected returns from a presumed efficient portfolio, in which most practitioners use some form of a market capitalization based portfolio as the presumed efficient portfolio. The practitioner can then adjust the reverse-optimized returns with his or her personal views. The fourth and final solution to this idea of nondiversified asset allocations is a technique called robust optimization. The third criticism of the MVO paradigm is that it relies on the first two moments of the return distribution namely, returns (the first moment) and variance and covariance (the second moment). Such events as the financial crisis of 2008 highlight that bad events occur in the market more often than is explained by the normal (bell-shaped) distribution. In reality, returns are not normally distributed for most asset classes, especially various alternative investments. Practitioners should be seeking tools that can accommodate so-called higher moments, such as skewness (third moment) and kurtosis (fourth moment). Fourth, traditional MVO considers the interrelationships in an asset-only (AO) context, ignoring frameworks oriented by liability-driven investment (LDI). LDI is important because almost all portfolios exist to pay for streams of future liabilities, so surplus optimization, or liability-relative optimization, is a more appropriate framework than an AO optimization. Finally, in recent years, two alternatives to the traditional MVO approach applied to asset classes have emerged and gained significant attention. The first, risk parity, abandons the traditional goal of attempting to maximize return per unit of risk and focuses exclusively on maximizing the diversification of risk. Risk parity attempts to overcome the criticism that traditional asset allocation leads to asset allocations that do not diversify sources of risk. The second alternative to the traditional approach, risk-factor-based asset allocation, is not necessarily in contrast to or a criticism of MVO; but rather it advocates replacing the traditional asset allocation building blocks of asset classes with risk factors in the optimization process (be it MVO or some other, more sophisticated approach). In my discussion of the two distinct topics of risk parity and asset allocation based on risk factors versus asset classes, I will highlight the work of two separate research papers that I coauthored with Maciej Kowara. Risk Parity. Risk parity portfolio construction explicitly ignores the expected returns of assets and focuses solely on measures of risk or diversification, an approach that makes sense if expected returns of assets are unpredictable or if the expected returns of all assets are the same. There are a number of different flavors of risk parity with different degrees of sophistication. Although it was not referred to as risk parity, the original and most simplistic version is equal weighting, or the so-called 1/N strategy. 2 December CFA Institute cfapubs.org

3 Evaluating New Methodologies in Asset and Risk Allocation A traditional 60% US equity/40% US bond portfolio is considered balanced but only from the perspective of returns. In a 60/40 portfolio, more than 90% of the total risk (expressed as standard deviation) comes from stocks. Advocates of risk parity argue that risk should come equally from both sources, which would result in a lower weight to equities. Then, to achieve a higher return or target expected return, investors can lever the portfolio with a short position in cash to meet a particular risk appetite. A shortcoming of most flavors of risk parity is that by changing the opportunity set to include or exclude any given asset class, investors might end up with an undesirable distribution of risks. For example, a common risk parity weighting scheme is to weight each asset class by the inverse of its standard deviation, scaled to 1, and then lever up the resulting portfolio. The primary problem with this approach is that it ignores correlations and, as a result, the portfolio weights are highly sensitive to the composition of the opportunity set. In the last five years or so, there has been a proliferation of literature dedicated to risk parity, arguing for and against it, which, again, is perhaps owing to the relative outperformance of bonds over equities. Prior to the publication of Asness, Frazzini, and Pedersen (2012), risk parity detractors were not sure what they were fighting against. They knew that they did not like risk parity, but no one had presented a viable theory of why risk parity might work. Asness et al. (2012) changed the risk parity debate, and I believe that their paper is the primary work supporting risk parity. From an empirical perspective, they have a long backtest that they claim produces statistically significant results, although I believe, as others do, that there is a serious flaw in their backtest. More importantly, from a theoretical perspective, they attach a theory called leverage aversion as an explanation for why risk parity might outperform other strategies, such as asset allocation models produced from traditional MVO. If investors are averse to leverage and they want their portfolios to have higher expected returns, then they are more likely to buy asset classes or securities that they believe have a higher expected return. Higher demand for higher expected return bids up the price. For individual securities, there is quite a bit of evidence that buying low-beta, low-volatility stocks produces better returns. At the asset class level, there really is not very much evidence of that. In a working paper from 2011, Kowara and I (2011) tested risk parity in two ways. First, we tried to directly test leverage aversion. By directly testing, I mean that rather than leveraging an arbitrary combination of stocks and bonds, such as the quintessential 60/40 mix that turns into a joint test of the weighting scheme, we instead levered up bonds to match the volatility of stocks based on volatility over a three-year rolling window. We assumed that the cost of levering (borrowing or shorting cash) was 60 bps above the 30-day US T-bill rate on an annualized basis. For this direct test, our monthly sample period was The first three years (36 monthly observations) of the sample were used to calibrate the standard deviation of stocks so that we could match it with levered bonds. For our second test of risk parity, we used a shorter set of available data and investigated whether a risk parity portfolio built using what we believe to be a truer implementation of the risk parity paradigm does indeed show superior performance. More specifically, in our paper, we introduced a technique for examining the true diversification of independent, or uncorrelated, sources of risk in a portfolio based on principal component analysis. Principal component analysis is a mathematical procedure that converts a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables referred to as principal components. This process leads to what we believe is a superior method for defining and measuring risk parity as well as building risk parity portfolios that more accurately capture the spirit of risk parity. This type of methodology is meant to dispel any suggestion that our opportunity set was not constructed in a thoughtful way and/or that it overcomes built-in biases that might be introduced from an opportunity set that included significantly more equity asset classes than fixed income, or vice versa. In-sample performance results of our direct test to the end of December 2010 are shown in Figure 1. Early in the sample period, levered bonds dramatically outperformed stocks. In the middle of the period, levered bonds dramatically underperformed as equities caught up. Since then, through 2010, the performance has been about the same. Factoring in 2011 and 2012 and some more recent data in an out-of-sample period equities have had a nice run and the performance gap has diminished significantly. We conclude that there is no statistical difference in performance between levered bonds and equities, which refutes the risk parity theory. There were periods when bonds had to be levered more than 25 times to match the risk of stocks. We were assuming that the annual financing rate for borrowing was about 60 bps above US T-bill rates. I suspect it would not have been possible to actually find lenders at that rate at that time with such dramatic leverage. Most of the backtests on risk parity that go back to the 1920s have to 2013 CFA Institute cfapubs.org December

4 CFA Institute Conference Proceedings Quarterly Figure 1. In-Sample Performance Results of Levered Bonds vs. Stocks, January 1929 December 2010 January 1929 = $1 10, , Levered Bonds Stocks Note: Returns are not statistically different at the normal confidence levels. Source: Kowara and Idzorek (2011). assume various borrowing rates, but it is impossible to know what would have been in place at the time at these types of leverage levels. Next, I will turn to our second test, in which we used a truer definition of risk parity. Our insample backtest started in 1976, and again, using principal component analysis, we tried to diversify the independent sources of risk associated with a long-only-oriented portfolio and then lever it up to meet the standard deviation of a static 50/50 portfolio. Oddly, as we did a better job of diversifying our independent sources of risk, the risk parity strategy actually underperformed the 50/50 portfolio. Again, I would count this result as evidence against risk parity. A truer, more sophisticated definition of risk parity performing worse does not bode well for the strategy. So, I believe that there is low or no statistical significance supporting risk parity. Earlier, I mentioned that I believed that the Asness et al. (2012) backtest was flawed. In Asness et al., the backtest was calibrated to the target volatility based on the full 85-year sample, a clear form of lookback bias, using data only available after the fact, in the data analysis that is, not a true out-ofsample test. This issue was recently highlighted in a Graham and Dodd Award winning article by Anderson, Bianchi, and Goldberg (2012), in which the authors corrected for lookback bias by using a three-year rolling standard deviation through time. Results that appeared to be statistically significant in Asness et al. are actually shown to be no longer statistically significant given this relatively minor change. So, the supposedly ironclad proof for risk parity that some researchers have claimed seems to have been eliminated or diminished. Risk Factors vs. Asset Classes Various asset managers have written marketingoriented pieces that have bothered me, and our recent Morningstar papers are a response to what I think are overhyped claims, which have likely confused investors, of the inherent superiority of asset allocation based on risk factors as opposed to asset classes. I coauthored a paper that we first called The Myth of Factor-Based Asset Allocation in 2011; the title is a play on words to refute one of the articles that I found most bothersome. Now, the title of that paper has evolved to a tameddown version: Factor-Based Asset Allocation vs. Asset-Class-Based Asset Allocation (2013), published in the Financial Analysts Journal. Our original title was motivated by one of the offensive articles, called The Myth of Diversification: Risk Factors versus Asset Classes (Page and Taborsky 2011). In that article, the authors argue that a move to risk factors from asset classes will result in an inherently superior asset allocation. I have nothing against carrying out asset allocation based on risk factors; I simply do not think that it is a silver bullet (i.e., a magical solution). I think the confusion around asset allocation based on risk factors is similar to what was happening a few years ago around the concept of portable alpha. The fact that alpha could be moved from one asset class to another did not magically or automatically produce alpha. It was just a technique, and the use of the technique does not in and of itself create alpha. If a practitioner is more comfortable predicting or forecasting the returns of factors as 4 December CFA Institute cfapubs.org

5 Evaluating New Methodologies in Asset and Risk Allocation opposed to asset classes, then I recommend working with factors. Prevalent in the literature on risk factors is the observation that the average pairwise correlation of various factors is much lower than that of asset classes. Again, proponents of risk factors are claiming that using them is more efficient. To be efficient, in my opinion, the efficient frontier would have to lead to either a higher expected return for any given level of risk or lower risk for any given return. A typical backtest that demonstrates the purported superiority of risk-factor allocation is shown in Figure 2 (Briand, Nielsen, and Stefek 2009). The 60/40 index is weighted 60% stock index and 40% bond index compared with a combination of risk premiums, including value, size, momentum, credit, high yield, and term spread, along with five hedge fund like strategies. The Sharpe ratio of the risk-factor index is more than three times as large as that of the asset classes. Note that the backtest ended on 2 January 2009, a time when equities had just plummeted in the aftermath of the financial crisis. I do not think that this is necessarily a fair comparison because they simply compared two asset classes against a wide variety of different exposures and strategies. In our recently published article on the subject, Kowara and I prove mathematically that there is no efficiency gain from using either factors or asset classes. Our 2013 paper includes real-world optimizations based on the asset classes and risk factors shown in Exhibit 1. There is no inherent advantage to one opportunity set versus the other. By allowing for shorting, the optimizer captures some of these risk premiums; the size premium goes long the Russell 2000 and short the Russell By allowing the optimizer to short asset classes, which is typically not done in practice, the strategy could synthetically create the size premium at any desired optimal level. As opposed to the short time period that is often backtested, our sample period was , and we conducted a long-only optimization, as shown in Panel A of Figure 3. Our decision may seem like a victory for asset classes, but it is not. We shortened our time period to focus on the most recent Figure 2. Cumulative Return of Traditional and Factor-Based Asset Allocation, May 1995 May = Risk Premium Index Source: Briand, Nielsen, and Stefek (2009). 60/40 Index Exhibit 1. Opportunity Sets Asset Classes Proxy Risk Factors Proxy Equity-oriented US large value Russell 1000 value Market Russell 3000 Citi 3-month Treasury US large growth Russell 1000 growth Size Russell 2000 Russell 1000 US small value Russell 2000 value Valuation Russell 3000 value Russell 3000 growth US small growth Russell 2000 growth Fixed-income-oriented US MBS BarCap US MBS Mortgage spread BarCap US MBS BarCap Treasury intermediate US Treasuries BarCap Treasury Term spread BarCap US Treasury 20+ year Citi 3-month T-bills US credit BarCap US credit Credit spread BarCap US credit BarCap Treasury Cash Citi 3-month T-bills Cash Citi 3-month T-bills Source: Idzorek and Kowara (2013) CFA Institute cfapubs.org December

6 CFA Institute Conference Proceedings Quarterly Figure 3. Arithmetic Annualized Return of Risk Factors vs. Asset Classes A. January 1979 December 2011 Arithmetic Annualized Return (%) Asset Classes (long only) Factors Annualized Standard Deviation (%) B. January 2002 December 2011 Arithmetic Annualized Return (%) Factors Annualized Standard Deviation (%) Source: Idzorek and Kowara (2013). Asset Classes (long only) 10 years and obtained a different result, as shown in Panel B of Figure 3. By simply cherry-picking different historical time periods for optimization, researchers can get the result that they are seeking. The key point here is that neither asset-class-based nor factor-based allocation is inherently superior. Liability-Relative Optimization I believe that all portfolios essentially exist to pay for a liability: to fund a pension for a retiree for a defined benefit pension plan, to cover living expenses for an individual investor, and so forth. A typical individual private wealth investor prior to retirement has three sources of liabilities namely, the present value of the following: 1. preretirement expenses 2. postretirement expenses 3. bequests (leaving money to beneficiaries through an estate) Of course, most of these are not legal liabilities, but in retirement, most investors want a real, inflation-adjusted income stream for life. This same private wealth investor also has assets. Obviously, the current value of the investor s financial capital is included on the balance sheet. In addition, the investor has human capital, which is the sum of the present values of the following: 1. earnings used for preretirement expenses 2. earnings directed toward savings 3. future earnings of Social Security and pensions Rather than focusing solely on the asset-only side of the balance sheet, I seek a holistic solution using liability-relative optimization. In addition, the opportunity set needs to include additional asset classes that would most likely result in an efficient frontier with better risk return tradeoffs. Liability-relative optimization is an extension of the Markowitz MVO approach that accounts for the fact that the portfolio exists to pay for a liability. In other words, it generates efficient asset allocations in the presence of a liability. We can force the optimizer to hold either a single asset class or a combination of asset classes representing the systematic characteristics of the liability and, in the presence of the liability with those systematic characteristics, attempt to set policy weights. In AO optimization, the optimizer would seek assets that have low correlation coefficients with each other. When considering the liability, the optimizer would seek assets that have high correlation with the liability. Figure 4 shows that when moving from AO space to liability-relative space, the liabilityrelative frontier dominates the AO frontier. The investor s liability has a negative return, which behaves like a fixed-income security with payments linked to inflation to cover cost-of-living increases in pre- and postretirement. Therefore, the liability behaves like a short Treasury Inflation-Protected Security (TIPS). Most of us only tend to look at performance in AO space and thus draw the opposite conclusion. Asset Allocation and Markowitz 2.0 Asset class returns are not necessarily normally distributed. I have co-authored three different papers on this topic with another one of my Morningstar coworkers, James Xiong. Assuming that one has some forecasting skill, anything above and beyond the first two moments of a return distribution (average and standard deviation) is an improvement over Markowitz December CFA Institute cfapubs.org

7 Evaluating New Methodologies in Asset and Risk Allocation Figure 4. Expected Return of Asset-Only Optimization vs. Liability- Relative Optimization Expected Return A. Traditional Asset-Only Space Asset-Only Frontier Liability-Relative Frontier TIPS 0 Retirement Income Liability (short TIPS-like characteristics) Standard Deviation or Conditional Value at Risk Expected Return B. Liability-Relative Space Liability-Relative Frontier Asset-Only Frontier 0 TIPS a Standard Deviation or Conditional Value at Risk a Being long TIPS offsets systematic retirement liability. Figure 5 is the well-known Ibbotson stocks, bonds, bills, and inflation chart that plots the cumulative performance of $1 invested in various asset classes starting in For example, $1 continuously invested in US small stocks would have been worth $18,365 by the end of This result implies an annual geometric average return of 11.9% over the same time period. The average does not adequately describe risk. To get a better idea of risk, I use the annual data for the S&P 500 Index from Ibbotson Associates. The data appear to be normally distributed, with a mean arithmetic annual return for the period of 11.8%. But the investor will not consistently earn 11.8% each year. For example, during the financial crisis of 2008, the return was 37%; it turned positive in 2009 at 26.5%. This example highlights the flaw of averages, a term used as the title for a book by Sam Savage (2009), in which he argues that basing investment decisions solely on the average expected conditions is flawed. Paul D. Kaplan (2009), another Morningstar colleague of mine, created a histogram using monthly returns instead of annual returns CFA Institute cfapubs.org December

8 CFA Institute Conference Proceedings Quarterly Figure 5. Cumulative Performance of $1 Invested at Various Rates, = $1 100, , Small Stocks 1, Large Stocks Treasury Bills Government Bonds Inflation Figure 6 compares a histogram of realized returns with a normal bell-shaped distribution, focusing on the left-hand side of the distribution. Looking at the left tail, the individual monthly returns exceed the thickness of that normal distribution, which is commonly referred to as a fat tail. Technically speaking, in statistics, it is called leptokurtosis (a kurtosis value greater than 3) and indicates that bad events are occurring more often than predicted by the normal distribution. In fact, empirically, bad events happen 10 times more often than predicted for the S&P 500 Index using the normal distribution. A standard measure of left-tail risk is value at risk (VaR), which identifies the worst return at a specific point in the tail, usually the worst 1% or 5% outcome. A slight improvement of left-tail risk for nonnormal returns is conditional value at risk (CVaR), which provides the probability-weighted return of the entire tail and better captures skew and kurtosis. Many asset classes display negative skew, meaning that there are more losses than gains; that result combined with leptokurtosis would mean those losses occur more often than expected from a normal distribution. I have now expanded the capital market assumptions to include not only expected returns, standard deviations, and correlations but also skewness and kurtosis, the nonnormal qualities associated with that return distribution. In optimization models in which risk is defined as CVaR, the resulting efficient frontier maximizes expected return per unit of risk for a nonnormal, asymmetrical distribution. In the presence of cash flows or investor withdrawals from the portfolio to cover liability needs, the path taken by investment returns matters. Figure 7 shows historical simulation results for a 60/40 portfolio initially valued at $1 million with a $50,000 inflation-adjusted withdrawal each year. If the returns are sequenced from best to worst, almost infinite wealth is created under these simulations. Using the actual history of results from 1926 to 2010, a client would run out of money about 33 years into the simulation. If he or she were unlucky and realized the worst possible sequence of returns, the portfolio would last only eight years. If one is drawing down a portfolio to pay for a liability (as discussed earlier), I recommend that the asset allocation of the portfolio be based on an optimization technique that attempts to avoid the severe downside risk. Figure 8 shows the probability of failure that is, the investor s portfolio runs out of money at some point in the future for any given constant monthly withdrawal rate. At one extreme, withdrawals of 0% have a 0% probability of failure. At the far right of Figure 8, withdrawals are large at 1% a month (12% annualized), which results in a 100% chance of failure. I am going to focus on a more realistic, yet extremely aggressive, withdrawal rate of 0.5% monthly (6% annualized). At this level, our analysis shows that the probability of failure using a traditional MVO (which ignores skew and kurtosis) asset allocation is pretty high, approximately 25%. When including the higher moments of skew and kurtosis and optimizing using CVaR, there is a 10 percentage point reduction in the failure rate. 8 December CFA Institute cfapubs.org

9 Evaluating New Methodologies in Asset and Risk Allocation Figure 6. S&P 500 Index Monthly Returns vs. Normal Distribution, January 1926 November 2008 Number of Occurrences Return (%) Normal Distribution S&P 500 Returns Source: Kaplan (2009). Figure 7. Historical Simulation Results for 60/40 Portfolio of $1 Million with $50,000 Inflation-Adjusted Withdrawal Every Year Return ($) 10,000,000,000 1,000,000, ,000,000 10,000,000 1,000, ,000 10,000 1, /40 Best-to-Worst Returns 60/40 60/40 Worst-to-Best Returns Year Note: The evolution of the starting $1 million is based on a weighted average of the underlying indices actual returns from 1 January 1926 to 31 December Portfolio Construction After the asset allocation framework is completed, the next stage is the portfolio construction problem, or how much to allocate to the individual investment vehicles. For this discussion, I will assume that these investment vehicles can be traditional mutual funds, exchange-traded funds (ETFs), hedge funds, or commodity trading advisers, rather than individual securities. Waring, Whitney, Pirone, and Castille (2000) is not well known by practitioners but, just like MVO is the gold standard for asset allocation, Waring et al. is the foundation for constructing fund-offunds-oriented portfolios. After solving for the client s strategic asset allocation, alpha-tracking error optimization can be used to determine the fund-specific portfolio. Alpha-tracking error optimization can be implemented with all passive managers, some 2013 CFA Institute cfapubs.org December

10 CFA Institute Conference Proceedings Quarterly Figure 8. Probability of Failure for Any Given Monthly Withdrawal Rate Probability of Failure (%) MVO Constant Monthly Withdrawal Rate (%) Mean CVaR combination of passive and active, or all active. So, every strategic asset allocation has its own implementation efficient frontier. The traditional efficient frontier is a combination of asset classes, whereas the implementation frontier concerns allocations to individual managers. Identifying better managers leads to a higher implementation frontier. The goal of the implementation frontier is to maximize the information ratio, which is the ratio of alpha to tracking error (also known as active risk). The goal of the traditional efficient frontier is to maximize the Sharpe ratio, which is the ratio of excess return (above the risk-free rate) to the standard deviation of the portfolio s excess returns. To my knowledge, in a fund-of-funds optimization context, almost no work has been done to create a next-generation framework for fund-specific optimization that goes beyond the assumption of a normal distribution. What is needed is a fundof-funds portfolio construction tool that considers skewness and excess kurtosis (fat tails), which is well suited for alternative investments, including hedge funds, managed futures, and private equity investment vehicles. At Morningstar, we are working on multiple papers and research projects to develop just such a fund-of-funds optimization framework. Early results suggest this is a fruitful area for further research. Additionally, given that the departure from the normal distribution is far more significant for strategies than it is for asset classes, incorporating higher moments into the fund-of-funds optimization procedure would seem to be far more important than incorporating higher moments into an asset allocation procedure. Conclusion Markowitz s original MVO framework is without a doubt the de facto standard for creating asset allocation models that attempt to maximize return per unit of risk. Nevertheless, it has a number of shortcomings for which there are viable solutions. Markowitz 2.0 is the framework that we at Morningstar have been using to build asset allocations; it goes beyond the first two return moments and incorporates nonnormal return characteristics into the optimization process. Risk parity is an alternative to MVO. Despite its link to the relatively elegant theory of leverage aversion, our research indicates that there is little to no evidence that risk parity has outperformed. Similarly, there is no inherent advantage to using either risk factors or asset classes over the other; neither is necessarily superior. In terms of liability-relative optimization, the industry has been tainted by asset managers that are constantly selling LDI-oriented techniques. The most elegant of the LDI frameworks is fullscale surplus optimization, or liability-relative optimization, which is appropriate for almost all individual and institutional portfolios that exist to pay for a liability. Finally, Markowitz 2.0 recognizes that returns are not normally distributed at the asset class level. This finding becomes more important when working with managers and strategies whose returns suffer from negative skew and excess kurtosis, such as alternative investments. This article qualifies for 0.5 CE credit. 10 December CFA Institute cfapubs.org

11 Evaluating New Methodologies in Asset and Risk Allocation REFERENCES Anderson, Robert M., Stephen W. Bianchi, and Lisa R. Goldberg Will My Risk Parity Strategy Outperform? Financial Analysts Journal, vol. 68, no. 6 (November/December): Asness, Clifford S., Andrea Frazzini, and Lasse H. Pedersen Leverage Aversion and Risk Parity. Financial Analysts Journal, vol. 68, no. 1 (January/February): Briand, Remy, Frank Nielsen, and Dan Stefek Portfolio of Risk Premia: A New Approach to Diversification. MSCI Barra Research Insight (1 January). Idzorek, Thomas M., and Maciej Kowara Factor-Based Asset Allocation vs. Asset-Class-Based Asset Allocation. Financial Analysts Journal, vol. 69, no. 3 (May/June): Kaplan, Paul D Déjà Vu All Over Again. Morningstar Advisor (February/March): Kowara, Maciej, and Thomas M. Idzorek Risk Parity and Leverage Aversion Revisited. Working paper, Morningstar Investment Management. Markowitz, Harry M Portfolio Selection: Efficient Diversification of Investments. Hoboken, NJ: John Wiley & Sons. Page, Sébastien, and Mark A. Taborsky The Myth of Diversification: Risk Factors versus Asset Classes. Journal of Portfolio Management, vol. 37, no. 4 (Summer):1 2. Savage, Sam L The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty. Hoboken, NJ: John Wiley & Sons. Sharpe, William F The Arithmetic of Active Management. Financial Analysts Journal, vol. 47, no. 1 (January/February):7 9. Waring, M. Barton, Duane Whitney, John Pirone, and Charles Castille Optimizing Manager Structure and Budgeting Manager Risk. Journal of Portfolio Management, vol. 26, no. 3 (Spring): CFA Institute cfapubs.org December

12 CFA Institute Conference Proceedings Quarterly Question and Answer Session Thomas M. Idzorek, CFA Question: Is there a lookback bias in your CVaR estimate? Idzorek: When setting asset allocation policy, historical returns, standard deviations, or correlations should not be used by themselves, if at all. The investor should use forwardlooking estimates of the distribution of returns. The cutting-edge practitioners seek to predict or forecast not only the first two moments of the distribution but also the conditional skewness or conditional kurtosis, resulting ultimately in a forward-looking estimate of the CVaR. The in-sample backtests are based on unconditional, realized data. But in a forward-looking setting, what really matters is the ability to forecast. Historical data can be used as a guide, but the forward-looking parameters will most likely be different from those observed historically. Question: If you think of the CML, which incorporates a riskfree asset into the Markowitz framework, is risk parity just moving farther out (right) along the CML by incorporating leverage? Idzorek: I think it could be thought of that way. My premise is that there is nothing in the risk parity approach to suggest that it should have the highest expected Sharpe ratio. If a standalone risk parity portfolio had the highest Sharpe ratio, then it would be the portfolio you would want to lever. Question: There are lengthy periods, such as the last three decades, in which bonds have outperformed stocks. Risk parity analysis often starts in the 1970s, conveniently. What are your thoughts about period specificity? Idzorek: Going back to 1926 produces the longest series of data that we have at our disposal at Ibbotson. Arguably, in the big picture, it really is a drop in the bucket. If you think about what has been going on in the bond market from the late 1970s to today, there has been a dramatic decrease in interest rates and bond yields. To me, this decrease has enabled risk parity to appear to thrive. It has done very well as interest rates have come down. But those interest rates can move quickly in the opposite direction, which suggests that portfolios should seek to reduce their exposure to fixed income. 12 December CFA Institute cfapubs.org