Measuring Risk and Return

Question 1

One-period Arithmetic rate of return

Answer 1

Rt = (Pt - Pt-1)/Pt-1

or with dividends

Rt = (Pt + Dt - Pt-1)/Pt-1

Percentage change

Question 2

One-period Geometric (continuously compounded) rate of return

Answer 2

Rt = ln(Pt/Pt-1)

or with dividends

Rt = ln(Pt+Dt/Pt-1)

Question 3

Explain the geometric (continuously compounded) rate of return

Answer 3

The rate of return needed to increase wealth by a certain amount if returns are constantly paid in infinitely small parts and constantly reinvested

Question 4

N-period return using one-period geometric return

Answer 4

Geometric return = Rg1 + Rg2 +…+ RgN

Question 5

N-period return using one-period arithmetic return

Answer 5

Arithmetic return = [(1+R1)(1+R2)…(1+Rn)] - 1

Question 6

Converting continuously compounded returns into arithmetic returns

Answer 6

R arith = e^(Rcont) - 1

Question 7

Converting arithmetic returns into continuously compounded returns

Answer 7

R cont = ln (1+R arith)

Question 8

Holding period yield

Answer 8

The yield an investor would obtain for holding the asset over a certain period of time

= (Income + Vt - Vt-1) / Vt-1
= Income / Vt-1 + (Vt-Vt-1) / Vt-1
= Income Return + Capital Gains Return

Question 9

Arithmetic Expected Return

Answer 9

= (R1 + R2 + … + Rn) / n

Question 10

Variance of a single asset (=(St dev)^2)

Answer 10

= [(X1 - Xbar)^2 + (X2 - Xbar)^2 + … + (Xn - Xbar)^2] / n

Question 11

Z transformation

Answer 11

z = (x-xbar)/st dev

Question 12

Correlation

Answer 12

= ρ = Cov(X,Y)/σxσy

Question 13

Covariance

Answer 13

= [(X1-Xbar)(Y1-Ybar)+…+(Xn-Xbar)(Yn-Ybar)]/n

Question 14

Expected Portfolio Return

Answer 14

= w1ER1 + w2ER2 + … + wnERn

Question 15

Portfolio Variance (for two assets only)

Answer 15

= w1^2Var(R1) + w2^2Var(R2) + 2w1w2*Cov(1,2)