Q1:

The table below sets out the monthly total return, market capitalization, and research spending for ten firms over the four months from January 2020 to April 2020 inclusive. Each figure was observed at the end of the corresponding month.

1. Calculate the value-weighted average returns in April 2020 for each of the quintile portfolios formed by sorting on lagged Research Spending. Use lagged market capitalization for calculating value-weighted returns. (Hint: There are five quintile portfolios, each containing one fifth of all the stocks.)

Jan Feb Mar Apr Firm1 Firm2 9% -9% -8% 10% -3% -10% 10% -10% Firm3 -3% -6% -1% -4% Monthly Return (%) Firm4 Firm5 Firm6 Firm7 5% 10% -3% 5% -7% 1% -2% -7% -7% 2% 0% -5% 4% 9% 8% -2% Firm8 10% 6% -7% 2% Firm9 Firm10 5% -10% 4% 9% 6% 10% 4% 4% Jan Feb Mar Apr Market Capitalization ($ bn) Firm1 Firm2 Firm3 Firm4 Firm5 Firm6 Firm7 Firm8 Firm9 Firm10 306 255 505 693 104 147 310 432 546 612 282 281475644 105 144 288458568667 273 252 470 107 144 274 426 602 734 300 227 451 623 117 156 268 434 626 763 599 0% 270 | Jan Feb Mar Apr Firmi | Firm2 Firm3 0% 11% 15% 1% 17% 4% 12% 1% 9% 18% 0% 13% Research Spending (%) Firm 4 Firm5 Firm6 Firm7 12% 17% 13% 4% 3% 20% 7% 4% 10% 15% 14% 2% 0% 14% 1% Firm8 7% 20% 3% 16% Firm9 Firm10 2% 3% 7% 0% 8% 4% 4% 18% Jan Feb Mar Apr Firm1 Firm2 9% -9% -8% 10% -3% -10% 10% -10% Firm3 -3% -6% -1% -4% Monthly Return (%) Firm4 Firm5 Firm6 Firm7 5% 10% -3% 5% -7% 1% -2% -7% -7% 2% 0% -5% 4% 9% 8% -2% Firm8 10% 6% -7% 2% Firm9 Firm10 5% -10% 4% 9% 6% 10% 4% 4% Jan Feb Mar Apr Market Capitalization ($ bn) Firm1 Firm2 Firm3 Firm4 Firm5 Firm6 Firm7 Firm8 Firm9 Firm10 306 255 505 693 104 147 310 432 546 612 282 281475644 105 144 288458568667 273 252 470 107 144 274 426 602 734 300 227 451 623 117 156 268 434 626 763 599 0% 270 | Jan Feb Mar Apr Firmi | Firm2 Firm3 0% 11% 15% 1% 17% 4% 12% 1% 9% 18% 0% 13% Research Spending (%) Firm 4 Firm5 Firm6 Firm7 12% 17% 13% 4% 3% 20% 7% 4% 10% 15% 14% 2% 0% 14% 1% Firm8 7% 20% 3% 16% Firm9 Firm10 2% 3% 7% 0% 8% 4% 4% 18%