# Index weights

I’m having trouble understanding the difference between price weighted, value/market-cap weighted and equal weighted indices. I’d really appreciate if someone could explain these terms with examples.

Thank you.

I’m patiently waiting for a response from the magician!

I was in class all day today and am exhausted. I’ll try to post something tomorrow.

OK, here goes:

We have three stocks – A, B, and C – and three indices – PWI (price-weighted), CWI (cap-weighted), and EWI (equal-weighted). The number of shares outstanding for each stock is:

• A: 10,000
• B: 500,000
• C: 1,000

The stock prices at times t = 0, 1, 2, 3, and 4 are, respectively:

• A: \$100, \$110, \$105, \$100, and \$115
• B: \$10, \$9, \$11, \$10, and \$12
• C: \$5, \$3, \$5, \$8, and \$7

Thus, for PWI, stock A will have the greatest weight: 10 times as much as B and 20 times as much as C

The market caps for the stocks at times t = 0, 1, 2, 3, and 4 are, respectively:

• A: \$1,000,000, \$1,100,000, \$1,050,000, \$1,000,000, and \$1,150,000
• B: \$5,000,000, \$4,500,000, \$5,500,000, \$5,000,000, and \$6,000,000
• C: \$5,000, \$3,000, \$5,000, \$8,000, and \$7,000

Thus, for CWI, stock B will have the greatest weight: 5 times as much as A and 1,000 times as much as C.

The stock returns at times t = 1, 2, 3, and 4 are, respectively:

• A: 10.0%, -4.6%, -4.8%, and 15.0%
• B: -10.0%, 22.2%, -9.1%, and 20.0%
• C: -40.0%, 66.7%, 60.0%, -12.5%

For EWI, all three stocks will have equal weight, but because stock C’s returns are the most volatile, they’ll tend to move the index more than stock A’s or stock B’s

The index values at times t = 0, 1, 2, 3, and 4 are, respectively:

• PWI: 100.00, 106.09, 105.22, 102.61, and 116.52
• CWI: 100.00, 93.31, 109.16, 100.05, and 119.18
• EWI, 100.00, 86.67, 111.03, 128.11, and 137.72

The index returns at times t = 1, 2, 3, and 4 are, respectively:

• PWI: 6.1%, -0.8%, -2.5%, and 13.6%
• CWI: -6.7%, 17.0%, -8.3%, and 9.1%
• EWI, -13.3%, 28.1%, 15.5%, and 7.5%

Unfortunately, I cannot plot these here. I’ll do that on my website in the next few days. You can throw these numbers into Excel and make some graphs to see what tends to track what; the results are interesting.

Thanks so much! I’ll graph these numers in Excel this weekend.

My pleasure.