FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
A regression of bond yield spread on leverage (L) and a crisis dummy D (1 during crisis) with an interaction is: Spread = 40 + 30*L + 25*D + 20*(D*L), where spread is in basis points and L is a ratio. For a firm with L = 2.0, how much higher is the predicted spread during a crisis than outside a crisis?
The crisis premium is 65 basis points. With the interaction term, the difference between regimes is the dummy coefficient plus the interaction coefficient times leverage: 25 + 20 × 2.0 = 65 bp. Using only the dummy coefficient, 25 bp, ignores the slope shift.
- A25 bp
- B65 bp
- C40 bp
- D90 bpCorrect
Explanation
The difference between regimes is 25 + 20*L = 25 + 40 = 65 bp for L = 2.0... check: 25 + 20*2 = 65, so the crisis premium is 65 bp. Outside crisis: 40 + 60 = 100; crisis: 40 + 60 + 25 + 40 = 165; difference 65 bp.
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