GMO Forecasting

Case: Grantham, Mayo, and Van Otterloo, 2012: Estimating the Equity Risk Premium [9-211-051].

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1 GMO (not graded)

This section is not graded, and you do not need to submit your answers. But you are expected to consider these issues and be ready to discuss them.

1. GMO’s approach.

   • Why does GMO believe they can more easily predict long‑run than short‑run asset‑class performance?

   • What predicting variables does the case mention are used by GMO? Does this fit with the goal of long‑run forecasts?

   • How has this approach led to contrarian positions?

   • How does this approach raise business risk and managerial career risk?

2. The market environment.

   • We often estimate the market risk premium by looking at a large sample of historic data. What reasons does the case give to be skeptical that the market risk premium will be as high in the future as it has been over the past 50 years?

   • In 2007, GMO forecasts real excess equity returns will be negative. What are the biggest drivers of their pessimistic conditional forecast relative to the unconditional forecast? (See Exhibit 9.)

   • In the 2011 forecast, what components has GMO revised most relative to 2007? Now how does their conditional forecast compare to the unconditional? (See Exhibit 10.)

3. Consider the asset‑class forecasts in Exhibit 1.

   • Which asset class did GMO estimate to have a negative 10‑year return over 2002–2011?

   • Which asset classes substantially outperformed GMO’s estimate over that time period?

   • Which asset classes substantially underperformed GMO’s estimate over that time period?

4. Fund performance.

   • In which asset class was GMWAX most heavily allocated throughout the majority of 1997–2011?

   • Comment on the performance of GMWAX versus its benchmark. (No calculation needed; simply comment on the comparison in the exhibits.)

2 Analyzing GMO

This section utilizes data in the file gmo_data.xlsx. Convert total returns to excess returns using the risk‑free rate.

1. Performance (GMWAX). Compute mean, volatility, and Sharpe ratio for GMWAX over three samples:

   • inception → 2011

   • 2012 → present

   • inception → present
     Has the mean, vol, and Sharpe changed much since the case?

2. Tail risk (GMWAX). For all three samples, analyze extreme scenarios:

   • minimum return

   • 5th percentile (VaR‑5th)

   • maximum drawdown (compute on total returns, not excess returns)
     (a) Does GMWAX have high or low tail‑risk as seen by these stats?
     (b) Does that vary much across the two subsamples?

3. Market exposure (GMWAX). For all three samples, regress excess returns of GMWAX on excess returns of SPY:

   • report estimated alpha, beta, and R²

   • is GMWAX a low‑beta strategy? has that changed since the case?

   • does GMWAX provide alpha? has that changed across subsamples?

4. Compare to GMGEX. Repeat items 1–3 for GMGEX. What are key differences between the two strategies?

3 Forecast Regressions

This section utilizes data in gmo_data.xlsx.

1. Lagged regression. Consider the regression with predictors lagged one period: $\( r^{SPY}_{t} \;=\; \alpha^{SPY,X} \;+\; \big(\beta^{SPY,X}\big)^\prime X_{t-1} \;+\; \epsilon^{SPY,X}_{t} \tag{1} \)\( Estimate (1) and report the **\)R^2\(**, as well as the OLS estimates for \)\alpha\( and \)\beta$. Do this for:

   • \(X\) as a single regressor, the dividend–price ratio (\(DP\))

   • \(X\) as a single regressor, the earnings–price ratio (\(EP\))

   • \(X\) with three regressors: \(DP\), \(EP\), and the 10‑year yield
     For each, report the \(R^2\).

2. Trading strategy from forecasts. For each of the three regressions:

   • Build the forecasted SPY return: \(\hat r^{SPY}_{t+1}\) (forecast made using \(X_t\) to predict \(r^{SPY}_{t+1}\)).

   • Set the scale (portfolio weight) to \(w_t = 100 \,\hat r^{SPY}_{t+1}\).

   • Strategy return: \(r^x_{t+1} = w_t\, r^{SPY}_{t+1}\).
     For each strategy, compute:

   • mean, volatility, Sharpe

   • max drawdown

   • market alpha

   • market beta

   • market information ratio

3. Risk characteristics.

   • For both strategies, the market, and GMO, compute monthly VaR at \(\pi = 0.05\) (use the historical quantile).

   • The case mentions stocks under‑performed short‑term bonds from 2000–2011. Does the dynamic portfolio above under‑perform the risk‑free rate over this time?

   • Based on the regression estimates, in how many periods do we estimate a negative risk premium?

   • Do you believe the dynamic strategy takes on extra risk?

4 Out‑of‑Sample Forecasting

This section utilizes data in gmo_data.xlsx. Focus on using both \(DP\) and \(EP\) as signals in (1). Compute out‑of‑sample (\(OOS\)) statistics:

Procedure (rolling OOS):

• Start at \(t=60\).

• Estimate (1) using data through time \(t\).

• Using the estimated parameters and \(x_t\), compute the forecast for \(t+1\): $\( \hat r^{SPY}_{t+1} \;=\; \hat \alpha^{SPY,X}_t \;+\; \big(\hat \beta^{SPY,X}_t\big)^\prime x_t \)$

• Forecast error: \(e^{forecast}_{t+1} = r^{SPY}_{t+1} - \hat r^{SPY}_{t+1}\).

• Move to \(t=61\) and iterate.

Also compute the null forecast and errors: $\( \bar r^{SPY}_{t+1} = \frac{1}{t}\sum_{i=1}^t r^{SPY}_i, \qquad e^{null}_{t+1} = r^{SPY}_{t+1} - \bar r^{SPY}_{t+1}. \)$

1. Report the out‑of‑sample \(R^2\) $\( R^2_{OOS} \;\equiv\; 1 - \frac{\sum_{i=61}^T \big(e^{forecast}_i\big)^2}{\sum_{i=61}^T \big(e^{null}_i\big)^2} \)\( Did this forecasting strategy produce a positive \)R^2_{OOS}$?

2. Redo 3.2 with OOS forecasts. How does the OOS strategy compare to the in‑sample version of 3.2?

3. Redo 3.3 with OOS forecasts. Is the point‑in‑time version of the strategy riskier?

5 Extensions (not graded)

1. CART. Re‑do Section 3 using CART (e.g., RandomForestRegressor from sklearn.ensemble). If you want to visualize, try sklearn.tree.

2. CART, OOS. Compute out‑of‑sample stats as in Section 4.

3. Neural Network. Re‑do Section 3 using a neural network (e.g., MLPRegressor from sklearn.neural_network).

4. NN & CART, OOS. Compute out‑of‑sample stats as in Section 4.