Module 1: Returns of Financial Assets & Instruments

What is the holding period total return formula?

R = (P1 - P0 + D) / P0

What is the price return formula?

r_price = (P1 - P0) / P0

What is the income return formula?

r_income = D / P0

How is total return split into components?

Total return = Price return + Income return

How do you calculate cumulative holding period return over multiple years?

HPR = (1+r1)(1+r2)...(1+rn) - 1

What is the arithmetic mean return formula?

Arithmetic mean = (r1 + r2 + … + rT) / T

What is the geometric mean return formula?

Geometric mean = [(1+r1)(1+r2)…(1+rT)]^(1/T) - 1

How do you calculate geometric mean from initial and final value?

Geometric mean = (Ending value / Beginning value)^(1/T) - 1

What is the relationship between arithmetic and geometric mean?

Arithmetic mean >= Geometric mean; equal if all returns are identical.

How do you annualise a periodic return?

Annualised return = (1 + periodic return)^c - 1; c = periods per year

How do you convert ordinary return to continuously compounded return?

r_cc = ln(1 + r)

How do you convert continuously compounded return to ordinary return?

r = e^(r_cc) - 1

How do continuously compounded returns combine across time?

Add the log returns: cumulative r_cc = r_cc1 + r_cc2 + …

What is the approximate nominal risk-free rate formula?

Nominal RF ≈ Real RF + Expected inflation

What is the exact real return formula?

Real return = (1 + nominal return) / (1 + inflation) - 1

What is the approximate real return formula?

Real return ≈ Nominal return - Inflation

What is the approximate required return formula?

Required return ≈ Real risk-free rate + Expected inflation + Risk premiums

What is the exact relative excess return formula?

Excess return = (1 + investment return) / (1 + benchmark return) - 1

What is the approximate excess return formula?

Excess return ≈ Investment return - Benchmark return

What is a risk premium?

Additional expected return required for bearing risk above a reference rate.

What are common equity risk premiums?

Market, size and value premiums.

What are common bond risk premiums?

Default, liquidity and maturity premiums.

What is the difference between gross and net return?

Gross = after trading costs, before management fees; net = after applicable fees.

What is the after-tax return formula with separate tax rates?

r_after-tax = r_price(1 - t_CG) + r_income(1 - t_D)

What is the real after-tax return formula?

Real after-tax return = (1 + nominal after-tax return) / (1 + inflation) - 1

What is the leveraged return on equity formula?

r_LP = r_P + (Debt / Equity)(r_P - borrowing rate)

When does debt leverage increase return on equity?

When portfolio return exceeds borrowing cost; losses are also magnified.

What are the payoff, profit and return formulas for a long call?

Payoff = max(S_T - K, 0); Profit = Payoff - Premium; ROI = Profit / Premium

What are the break-even price and maximum loss for a long call?

Break-even = Strike + Premium; maximum loss = Premium paid.