Forecasting Tools

1. Statistical Tools:

1. Projecting historical data
1. GM<AM when variance goes higher
2. Shrinkage Estimators
1. Weighted average of historical covariance and estimated in factor model
2. Weighted average of historical return of the asset and the historical return of other assets
3. Time Series Analysis
1. E.g. variance(t+1) = a*variance(t)+(1-a)*error(t)^2
2. Larger a, more volatility clustering
4. Multifactor Model
1. Ri=ai+Betai1*F1+Betai2*F2+error_i
2. Rj=aj+Betaj1*F1+Betaj2*F2+error_j
3. Var(i)=Betai1^2*Var(F1)^2+Betai2^2*Var(F2)^2+2*Betai1*Betai2*Cov(F1,F2)+error_i^2
4. Cov(i,j) = Betai1*Betaj1*var(F1)^2+Betai2*Betaj2*var(F2)^2+(Betai1*Betaj2+Betai2*Betaj1)*Cov(F1,F2)

*** If no partial covariance (Betai equal to zero), doesn’t mean that the return has no correlation to the factor. It is just that it has no sensitivity when the other factors are in controlled!

2. Discounted Cash Flow Model

Required Rate of Return (Grinold and Kroner)

R = Div1/P0 + g + inflation – delta (outstanding stock) + change of P/E

With repurchasing yield and repricing

Fed Model: compare the earning yield to 10-year Treasury Bond. If less, investor will shift to T-bond.

3. Risk Premium Approach:

Real risk-free rate + inflation rate + default risk premium + liquidity risk premium + maturity risk premium + tax premium

4. Financial Equilibrium Models

ICAPM: Ri = R_rfr + Beta_i* (R_GM – R_rfr)

rou(i,m) = cov(i,m)/sigma(i)sigma(m)

Beta_i = Cov(i,m)/var(m)

ERP_i = rou(i,m)*sigma(i) *ERP_m/sigma(m)

ERP = Equity Risk Premium

Fully Segmented: rou(i,m) =1

Use weighted average of Fully Segmented and Fully Integrated to find the ERP

5. Survey or judgement