Regression Diagnostics in a Korean Equity Hedge Fund
A Seoul-based equity long-short fund reports monthly performance attribution using 72 months of data. The risk analyst estimates a four-factor model: excess fund return on the KOSPI excess return, size (SMB), value (HML), and monthly KRW depreciation against the USD. The output shows alpha of 0.42% per month with a t-statistic of 1.15; market beta 0.86 (t = 3.10); SMB 0.47 (t = 2.35); HML -0.18 (t = -0.72); KRW beta 0.39 (t = 3.62); R-squared 0.71. Diagnostics: Durbin-Watson 0.58; Breusch-Pagan test p-value 0.018; variance inflation factors of 9.6 for market beta and 8.9 for SMB. The fund's marketing deck says the model proves 'statistically significant alpha and no material factor biases.' An investment committee member asks whether the alpha and the KRW exposure are reliable, and whether the model can be used to set a hedge ratio for next month.
1. Interpret the Durbin-Watson, Breusch-Pagan, and VIF results. What are the consequences for the reported t-statistics and the alpha claim?
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DW=0.58 is far below the no-autocorrelation benchmark of about 2 and indicates strong positive serial correlation. OLS standard errors are understated, so the reported t-statistics are inflated. The alpha t of 1.15 is already insignificant, and after a Newey-West correction it would be weaker, so the claim of significant alpha is unsupported. Breusch-Pagan p=0.018 rejects homoskedasticity; heteroskedasticity also makes conventional standard errors unreliable and calls for robust or weighted least squares. VIFs near 9-10 indicate severe multicollinearity between market beta and SMB, so their individual coefficients and t-stats are unstable even though the joint model may fit. The KRW beta t=3.62 is the strongest result, but serial correlation still inflates it; it should be re-tested with HAC errors. The marketing deck's statement is not supported; the model needs diagnostics before any factor-bias claim.
2. The committee wants a one-month forecast. Suppose next month's KOSPI excess return is 1.8%, SMB is 0.4%, HML is -0.5%, and KRW depreciation is 1.2%. Compute the point forecast and explain why the interval is wider than the regression's standard error suggests.
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Forecast = 0.42 + 0.86(1.8) + 0.47(0.4) - 0.18(-0.5) + 0.39(1.2) = 0.42 + 1.548 + 0.188 + 0.09 + 0.468 = 2.714%, about 2.71%. This is a mechanical point forecast from unstable coefficients. The interval should be wider than the regression standard error because (i) positive autocorrelation means residuals are not independent, (ii) heteroskedasticity means error variance changes, (iii) multicollinearity makes coefficient estimates imprecise, and (iv) the alpha is insignificant, so the intercept is not reliably different from zero. It also assumes the factor realizations are known, which they are not. For hedge-ratio use, the KRW beta of 0.39 is statistically strongest but may be capturing omitted global risk factors. Use out-of-sample rolling estimation and HAC standard errors; do not treat 2.71% as a precise expected return.
3. Recommend concrete model fixes and state how each could change the interpretation of the KRW beta and the hedge ratio.
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Use Newey-West HAC standard errors and re-test all coefficients; if autocorrelation remains, estimate an AR(1) or dynamic model. Address heteroskedasticity with robust or GLS estimation. For multicollinearity, either orthogonalize SMB versus market, drop one factor if economically redundant, or use ridge/principal components; interpret individual betas cautiously. Use rolling windows or Kalman-filtered time-varying betas for hedge ratios, because a static 72-month beta may not represent next month. Add out-of-sample validation and report prediction intervals. The KRW beta may fall in significance after HAC correction; if it survives, hedge the currency exposure with a separate overlay rather than embedding it in the equity factor model. If it does not survive, the apparent KRW exposure may be spurious. Any hedge ratio should be based on the corrected model and monitored.