Moderator: Dirk Cotton Speaker: Huy Lam, CFA, Senior Analyst at Schultz Collins, Inc. Measuring risk of ruin with retirement risk models: What is the evidence for implicit over-optimism in commonly used risk models? Presented by: Huy Lam, CFA

Summary Situation: Having a successful retirement is a critical portfolio objective for retired investors. Complication: Implausible assumptions underlying common risk models may mislead investors concerning the risk and return expectation of their retirement investment strategies. Importance: As practitioners and academics, we want to help investors make informed financial decisions that will lead to a more successful retirement. Solution: An array of more plausible alternative modeling tools already exists that can help retirees plan their retirement.

Successful retirement Successful retirement requires correctly determining the portfolio's planning horizon, asset allocation, and withdrawal strategy A definition of successful retirement: The portfolio value is greater than zero at the end of the planning horizon (not going “bankrupt”). Other definitions: Min bequest amount Max withdrawals Some combination Etc… Planning Horizon (Pre-specified Fixed Period or Conditional on Longevity) Distribution Strategy (Consumption and Terminal Wealth Goals) Asset Allocation (Investment of Initial Wealth and Ongoing Asset Management Elections) Successful retirement

The planning horizon determines how long the portfolio needs to last Fixed horizon - known planning horizon For retirees, fixed planning horizons are typically based on life expectancy Individual lifespan – introduces an uncertain planning horizon Age Gender (women typically live longer than men) Profession (white collar workers typically live longer than blue collar workers) Etc… Join lifespan – expands the uncertain planning horizon to individual and joint uncertainty Couples, intergenerational family members, etc… Perpetuity – extremely long term planning horizon (100+ years) Permanent endowments, perpetual trusts, dynasty trusts, etc…

The asset allocation encompasses portfolio management elections such as asset position, asset location, rebalancing strategy, etc… Asset position – determines point in time risk exposure The percentage of the portfolio that is long/short in stocks, bonds, derivatives, etc… Asset location – determines the taxability Brokerage accounts, tax-deferred accounts, tax-exempt accounts, trusts, etc… Rebalancing strategy – determines risk exposure through time Constant Mix – maintain risk exposure [rebalance back to original asset allocation] Calendar rebalancing - shorter periods reduce drift, but increases trading cost Threshold rebalancing – smaller thresholds reduce drift, but increases trading cost Asset allocation level, asset class level, investment level Buy & Hold – losses reduce risk and gains increase risk; low trading cost Constant Proportion Portfolio Insurance (CPPI) – similar to Buy & Hold, but risk level changes at faster rates as increase s; high trading cost

The distribution strategy accounts for how and when periodic withdrawals are taken, and accounts for terminal wealth objectives Fixed amount withdrawal Percentage of portfolio value withdrawal Smoothed portfolio value A combination of a fixed amount and a floating amount withdrawal Front loaded withdrawals Back loaded withdrawals Etc…

Modelers need to understand the sources of model risk that arise from variable choice, input sensitivity, model structure, and model assumptions Some sources of model risk: Variable choice: what variables are important and can we model them? Input sensitivity: small input change leads to large changes in results Model structure: misspecification of variable interaction Model assumptions: characteristics of the variables of interest From a practitioner’s point of view, there are other considerations: Bonini’s paradox: A model is an imperfect representation of a more complex reality. As a model of a complex system becomes more complete, it becomes less understandable; for it to be more understandable, it must be less complete. Preference ranking: How does an individual rank different outcomes from equally credible models? How does an individual rank outcomes sets?

Along with the policy decisions, practitioners must also address the asset returns generating process Some well known approaches for modeling the outcome of asset returns can typically be categorized as one of the following approaches: Analytic formulae (closed form solutions) Historical back testing (rolling period returns) Bootstrapping (reshuffled historical returns) Monte Carlo simulation (assuming normality) Simulation of non-normal distributions Vector autoregression Regime-switching simulation Portfolio depletion rates are only as good as the models they are based on and are subject to “model risk”.

Date of portfolio depletion dependent on rate of return assumption Analytic formula provides a single outcome, given a set of inputs 𝑡= 1 𝑟 𝑙𝑛 𝑐 𝑐−𝑊𝑟 “An equation can’t predict your future… but it can help you plan for it” -Moshe A. Milevsky The 7 Most Important Equations For Your Retirement Date of portfolio depletion dependent on rate of return assumption

Historical back testing of empirical returns provides a few more outcomes by looking at small intervals over a long history Historical back testing yields multiple outcomes by calculating over smaller planning horizons of a long historical return series A new time period is added at every iteration The oldest time period is dropped at every iteration Historical Returns Series Iteration 1 of Planning Horizon Iteration 2 of Planning Horizon Iteration 3 of Planning Horizon

Bootstrapping provides a large number of outcomes by sampling from historical distribution Random draws from the historical distribution of actual asset returns at each time period Generated periodic returns for a single trial Historical distribution of asset returns Negative Returns Positive Returns

Monte Carlo simulation (assuming normality) provides an infinite set of outcomes Random draws from the underlying distribution of probable asset returns at each time period Generated periodic returns for a single trial The underlying distribution of probable returns Negative Returns Positive Returns

Examples of alternative non-normal distributions Simulation of non-normal distributions allows for more complex models of the variables of interests Bell shape curve underrepresents the frequency of severe negative returns. Average Standard Deviations Examples of alternative non-normal distributions Laplace Logistic Rayleigh Wakeby Etc…

Vector autoregression models are often too complex Vector autoregression allows for stochastic variables of interest Vector autoregression models are often too complex

Regime-switching simulation allows variables of interest to have different characteristics in different states The underlying distribution of probable bull market returns In regime switching models, random draws are taken from different distributions depending on the current, random state of the trial A single trial as a mixture of normal distributions The underlying distribution of probable bear market returns Negative Returns Positive Returns Bull Market Regime Bear Market Regime Bear Market Regime

Comparison of the modeling approaches

Size of possible outcomes of each modeling approach A comparison of the widely used Monte Carlo simulation approach against the regime-switching simulation approach Models of returns to compare: Normal Distribution Historical Model (denoted “NH”) Normal Efficient Returns Model (denoted “NE”) Regime Switching Model Market Agnostic (denoted “BB”) Regime Switching Model Bull Market Prediction (denoted “Bull”) Regime Switching Model Bear Market Prediction (denoted “Bear”) Size of possible outcomes of each modeling approach

Stochastic Previous 12 Months A note on inflation: it’s modeled as a stochastic random variable Inflation is modeled as a “sticky” random variable, because it is not constant nor completely random. However, inflation is often modeled as a constant. The following comparisons assume: A $1,250,000 portfolio with two asset class, allocated 70% stock and 30% bonds, ignoring investment fees, transaction costs, and assumed taxes. Annual inflation-adjusted withdrawal of $60,000 for 30 years. Model Statistic Constant 3% Inflation Constant 4% Inflation Constant 5% Inflation Stochastic Long Term Average Stochastic Previous 12 Months Ending Wealth at the 50th Percentile $2,417,712 $1,347,812 $665,967 $1,050,470 $1,423,391 Ending Wealth at the 30th Percentile $1,232,951 $499,252 $33,002 $129,020 $397,651 Ending Wealth at the 10th Percentile $71,029 $0 Bankruptcy 9% 18% 29% 26% 21% Assets Ever < $750k Inflation Adjusted 27% 43% 57% 51% 44%

Building models by adding layers of complexity A simple two asset class portfolio (denoted “S”) US stocks and bonds A diversified, multi-asset class, portfolio (denoted “D”) 14 asset classes: US, international, and REITs tilts in size, value, and duration A diversified portfolio with simulated longevity (denoted “DL”) 68 year old female in excellent health A diversified portfolio with simulated longevity and a predefined schedule of investment fees and transaction costs (denoted “DFL”) Progressive fee schedule Low investment and transaction cost A diversified portfolio with simulated longevity and a predefined schedule of investment fees, transaction costs, and assumed taxes (denoted “DFTL”) Taxes: 20% income rate; 15% capital gains; etc…

A simple two asset class model overestimates bankruptcy risk relative to a diversified portfolio model and a diversified portfolio model with longevity A simple two asset class model overestimates bankruptcy risk Diversification reduces bankruptcy risk, but is less effective in regime switching models, regardless of initial state (BB, Bull, Bear). This is due to dynamic correlation A 30 year time horizon overstates risk for a 68 year old female in excellent health, due to a life expectancy of roughly 19 years only

Portfolio frictions (fees & taxes) will raise bankruptcy risk, but they may be difficult to model accurately Ignoring fees and taxes underestimates bankruptcy risk Bankruptcy rates increase when fees and investment costs are taken into account, especially when the regime-switching model starts in a bear market Including taxes significantly increases bankruptcy rates, but taxes can be extremely difficult to model

Bottom line: investors and practitioners must be aware of the uncertainties in both the data and the risk model that incorporate it! The range of model bankruptcy rates is huge: 4% failure to 49% failure. With fast computers, what accounts for the propensity to use oversimplified risk models? Do practitioners “play it safe?” That is, if an investment strategy fails, the practitioner can find solace in the failures of others who used the same model. Any questions?

So the tools help us make decisions, but how do we make decisions about how to use the tools? Economist viewpoint. Psychologist viewpoint.

Schultz Collins, Inc. 455 Market Street, Suite 1250 San Francisco, CA 94105 Measuring risk of ruin with retirement risk models: What is the evidence for implicit over-optimism in commonly used risk models? Presented by: Huy Lam, CFA