1	Better Compound Growth Through Risk Management
2	The Rationale for Risk Management is Better Compound Growth How to get inferior results: GICS as savings plans LTCM over-leverage Telecommunications mania Even good tools need guidance: Optimal Asset Allocation Risk budgets Value-at-Risk Risk fundamentals: Volatility drives down median results One succeeds by growing discretionary wealth, or the margin of safety How should these principles affect risk management?
3	Risk Interferes With Compounding If you invest $1 in a leveraged hedge fund whose return each year is an equal chance of: 100% -50% What return do you expect to get each year? 100/2 + -50/2 = +25% What distribution of wealth will you actually achieve in 10 years? How could you improve the median result?
4	Appropriate Constant Leverage Monte Carlo simulation of the impact of different leverages where: Log-normal returns Mean excess stock return: .06 Return variance: .20² Leverages = 0.75, 1.5, 3.0 Rule of thumb: set your leverage ratio at excess return mean divided by variance, here .06/.04 = 1.5. This leverage ratio should be applied only to your margin of safety or discretionary wealth. Example: 40% discretionary wealth here implies a 60% allocation to stocks.
5	Comparing Active Managers Should we always rank active managers based on information ratios? Manager A: alpha 6%, tracking error 8%, IR=0.75. Manager B: alpha 5%, tracking error 1%, IR=5.0 Who would better manage your entire portfolio? Extending our prior example indicates A. Median return predicted from growth model: mean total return – variance/2. IR didn’t take into account leverage inflexibility.
6	Downside Protection With Constant Proportion Portfolio Insurance: CPPI Fraction in stocks = k(wealth-floor) Typical: k=5 floor=0.8initial wealth Constraint against borrowing Why do a large number of users get stuck, in real terms, near the floor?
7	The Hidden Problem of CPPI and Other Dynamic Hedging Programs Most of the investment literature focuses on the obvious problems created by pricing jumps and illiquidity. But if one focuses on the expected growth rate of the safety margin … It is also clear that the amplification of the impact of price moves on holdings (leverage) is often too high. Resulting in negative expected growth of the margin of safety.
8	What Growth Theory Says About Rebalancing vs. Stop-Loss Rules Rebalance: Among risky assets for efficient diversification Between cash and risky assets when excess return mean is less than its variance when the impact on your margin of safety is compensated by changes in expected returns. Follow stop-loss rules between risky assets and cash for losses and raise risk allocation after gains when all these conditions prevail: Your gains and losses are not compensated by changes in expected return Excess return mean is greater than its variance. Position amplification relative to returns is not excessive relative to optimal leverage.
9	Warning: Sometimes Return Mean and Variance are not Enough ... Total portfolio VaR shows substantial negative skew, as when writing index calls, or very fat-tailed return distributions, as when hedging using uncertain return correlations, or … Risky asset exposure relative to the margin of safety must be held at far-above-normal leverage ratios, or … Considering costly portfolio insurance. For these cases, you need to quantify the impact of return skew and kurtosis on median compound outcomes. That is, more fully consider downside risk.
10	Where Growth Models Can Help Manage Risk: Selecting the most appropriate risk tolerance in asset allocation studies. Quantifying the long-term growth benefits of diversification. Assessing the contribution of active managers. Deciding when to re-balance risky assets. Reacting to major changes in margin of safety. Designing better downside protection.