Reading 46: Security Market Indices

Question 1

Value of a Price Return Index

46.1

Security Market Indices

Answer 1

Where:

V_PRI = the value of the price return index

n_i = the nubmer of units of constituent security i held in the index portfolio

N = the number of constituent securities in the index

P_i = the unit price of constituent security i

D = the value of the divisor

Question 2

Price Return of an Index (single - period)

46.2

Security Market Indices

Answer 2

Where:

PR_I = the price return of tehn index portfolio (as a decimal number, i.e. 12 percent is .12)

V_PRI1 = the value of the price return index at the end of the period

V_PRI0 = the value of the price return index at the beginning of the period

Question 3

Price Return of Each Constituent Security

46.3

Security Market Indices

Answer 3

Where:

PR_i = the price return of constutent security i (as a decimal number)

P_i1 = the price of constituent security i at the end of the period

P_i0 = the price of constituent security i at the beginning of the period

Question 4

Price Return of Index Equals Weighted Average of Price Returns of Individual Securities

46.4

Security Market Indices

Answer 4

Where:

PR_I = the price return of index portfolio (as a decimal number)

PR_i = the price of constituent security i (as a decimal number)

N = the number of individual securities in the index

w_i = the weight of security i (the fraction of the index portfolio allocated to security i)

P_i1 = the price of constituent security i at the end of the period

P_i0 = the price of constituent security i at the beginning of the period

Question 5

Simplified Weighted Price Return of Index Portfolio

46.5

Security Market Indices

Answer 5

Where:

PR_I = the price return of index portfolio (as a decimal number)

PR_i = the price of constituent security i (as a decimal number)

N = the number of individual securities in the index

w_i = the weight of security i (the fraction of the index portfolio allocated to security i)

Question 6

Total Return of an Index

46.6

Security Market Indices

Answer 6

Where:

TR_I = the total return of the index portfolio (as a decimal number)

V_PRI1 = the value of the price return index at the end of the period

V_PRI0 = the value of the price return index at the beginning of the period

Inc_I = the total income (dividend and/or interest) from all securities in the index held over the period

Question 7

Total Return of Each Constituent Security in an Index

46.7

Security Market Indices

Answer 7

Where:

TR_i = the total return of the constituent security i (as a decimal number)

P_1i = the price of constituent security i at the end of the period

P_0i = the price of constituent security i at the beginning of the period

Inc_i = the total income (dividend and/or interest) from security i over the period

Question 8

Total Return of an Index Calculated as the Weighted Average of Total Returns of the Constituent Securities

46.8 and 46.9

Security Market Indices

Answer 8

Where:

TR_I = the total return of the index portfolio (as a decimal number)

TR_i = the total return of constituent security i (as a decimal number)

w_i = the weight of security i (the fraction of the index portfolio allocated to security i)

N = the number of securities in the index

Question 9

Value of Price Return Index Over Multiple Time Periods

46.10

Security Market Indices

Answer 9

Where:

V_PRI0 = the value of the price return index at inception

V_PRIT = the value of the price return index at time t

PR_IT = the price return (as a decimal number) on the index over period t, t=1, 2, …, T

Question 10

Value of Total Return Index by Series of Total Returns

46.11

Security Market Indices

Answer 10

Where:

V_TRI0 = the value of the price return index at inception

V_TRIT = the value of the price return index at time t

TR_IT = the price return (as a decimal number) on the index over period t, t=1, 2, …, T

Question 11

Price Weighting

46.12

Security Market Indices

Answer 11

Where:

P_i = Price of constituent security i

Question 12

Equal Weighting

46.13

Security Market Indices

Answer 12

Where:

w_i = fraction of the portfolio that is allocated to security i or weight of security i

N = number of securities in the index

Question 13

Market-Capitalization Weighting

46.14

Security Market Indices

Answer 13

Where:

w_i = fraction of the portfolio that is allocated to security i or weight of security i

Q_i = number of shares outstanding of security i

P_i = share price of security i

N = number of securities in the index

Question 14

Float-Adjusted Market-Capitalization Weighting

46.15

Security Market Indices

Answer 14

Where:

f_i = fraction of shares outstanding in the market float

w_i = fraction of the portfolio that is allocated to security i or weight of security i

Q_i = number of shares outstanding of security i

P_i = share price of security i

N = number of securities in the index

Question 15

Fundamental Weighting

46.16

Security Market Indices

Answer 15

Where:

F_i = a given fundamental size measure of company i

w_i = fraction of the portfolio that is allocated to security i or weight of security i

N = number of securities in the index