Index Value

1. Please answer the question and show your work.
1) A benchmark index has three stocks priced at $30, $40, and $50 yesterday. The number of outstanding shares for each is 100 shares, 200 shares, and 300 shares, respectively. The value weighted index was 100 yesterday and the prices changed to $27, $38, and $55 today.
I) What is the new index value? (15points)
II) What is the return on the index? (15points)
2) You sell short 1 share of ABC stock at $40 per share. The initial margin is 50% and the maintenance margin is 30%.
I) How much do you have at the margin account including your initial margin? (15points)
II) At what price will you get a margin call? (15points)
3) Consider a no-load mutual fund with the net asset value (NAV) of $10 at the start of the year. At the end of the year, the mutual fund has $288 million in assets with 24 million shares and its total expense ratio is 5%.
I) What is the NAV at the end of the year? Please take into account the expense ratio. (15points)
II) During the year, investors have received income distributions of $2 per share and capital gain distributions of $1.2 per share. What is the rate of return on the fund? (15points)
List of Formulas
1) Price-weighted index:

Sum of different stock prices

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# of kinds of stocks

2) Equal-weighted index:

Sum of ending balances for a stock
Sum of equal investments for a stock
×beginning index value

3) Value-weighted index:

n
∑(# of stock ×new price )
i                                                  ×beginning index value
n
∑(# of stock i ×old price i )
i

4) Margin requirement for margin trading:

[stock price−borrowing] = M

stock price

5) Margin requirement for short sale:

[cash balance−stock price] = M

stock price

6) Net asset value (NAV):

NAV= Asset/# of outstanding shares

7) Rate of return for mutual fund:

[NAV 1 − NAV 0 + income + capital gain distribution]/NAV 0

NAV1: net asset value at the end, NAV0: net asset value at the beginning. For more information on Index Value visit this: https://en.wikipedia.org/wiki/Index_(economics)

Index Value

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