Finance with Dr. John Elder
LE#3
Before starting these exercises, be sure to work through the examples in the notes and from the chapter!   

Chapt 4 #  1,3,4,6,7,13,14,17,19,20
These are some numerical problems associated with mutual funds.  We did not explicitly address numerical problems during class, but I have provided the solutions below so that you can work through them.
Stock trading:  Add an ETF or Mutual fund to your portfolio at OTIS.   Good sources of information on mutual funds are http://www.morningstar.com and http://finance.yahoo.com.  You may also use the screener to add a mutual fund to your portfolio. State the justification for your purchase in one typed paragraph and record this in your OTIS "journal". Note:  OTIS sometimes has trouble recognizing mutual fund ticker symbols.  As an example, the ticker for Vanguard Capital Opportunity Fund is VHCOX.  To get OTIS to recognize this ticker you must enter VHCO.X   (note the "." before the X).  On the other hand, OTIS immediately recognizes VFINX as Vanguard SP500 Index fund.  If your mutual fund is not being recognized by OTIS, try a "." prior to the final letter (usually an "X").   You can view the available mutual funds in the OTIS database under Analytics > Security list. (Note: trying to add the mutual fund to the OTIS database does not seem to work -- that is,  going the "Trade equities" page and clicking "Can't find an equity in OTIS? Add it to the OTIS database" does not seem to work.

Answers
1. The unit investment trust should have lower operating expenses.  Because its portfolio is fixed once the trust is established, it does not have to pay portfolio managers to constantly monitor and rebalance the portfolio as perceived needs or opportunities change.  Because its portfolio is fixed, the unit investment trust also incurs virtually no trading costs.
3. NAV = $11.69
4. NAV = $10.49
6. a. NAV = $39.40
    b. Premium is 8.6% discount from NAV
7. Rate of return = 8.8%
13. Start of year NAV = $20
       Dividends per share = $.20
       End of year NAV is based on the 8% price gain, less the one percent 12b-1 fee:
       End of year NAV = $20*(1.08)* (1 – .01) = $21.384
        Rate of return = ($21.384 – $20 + $0.20) / $20  =  .0792  =  7.92%
14. The excess of purchases over sales must be due to new inflows into the fund.  Therefore, $400 million of stock previously held by the fund was replaced by new holdings.  So turnover is: ($400/$2,200) = 0.182 = 18.2%
17.    Suppose you have $1000 to invest.  The initial investment in Class A shares is $940 net of the front-end load.  After 4 years, your portfolio will be worth:  $940*(1.10)4 = $1,376.25

Class B shares allow you to invest the full $1,000, but your investment performance net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you sell after 4 years.  Your portfolio value after 4 years will be:
    $1000*(1.095)4 = $1,437.66
    After paying the back-end load fee, your portfolio value will be:
    $1,437.66*0.99 = 1423.28
    Class B shares are the better choice if your horizon is 4 years.

    With a 15-year horizon, do this on your own.

19a. After 2 years, each dollar invested in a fund with a 4% load and a portfolio return equal to r will grow to:  $.96 * (1 + r – .005)2.  Each dollar invested in the CD will grow to $1 * (1.06)2.  If the mutual fund is to be the better investment, then the portfolio return, r, must satisfy
    0.96 *(1 + r – .005)2  >  (1.06)2.
    0.96 * (1 + r – .005)2  > 1.1236
    (1 + r – .005)2  > 1.1704
    1 + r – .005  > 1.0819
    1 + r  > 1.0869
    or r  >  0.0869 = 8.69%.

b. do this on your own.
c. do this on your own.

20.    The turnover rate is 50%.  This means that, on average, 50% of the portfolio is sold and replaced with other securities each year.  Trading costs on the sell orders are 0.4%; and the buy orders to replace those securities entail another 0.4% in trading costs.  Total trading costs will reduce portfolio returns by: (2 * 0.4% * 0.50) = 0.4%