1. [No Excel] I invested in the Fidelity Low Price Stock Fund in 2017. Suppose t

ID: 2818073 • Letter: 1

Question

1. [No Excel] I invested in the Fidelity Low Price Stock Fund in 2017. Suppose the prices of the fund were $45.50, $47.80, $49.60, $52.00, and $56.9 at the beginning of January, April, July, October, and January 2018, respectively. In addition, it also paid S4 dividends at the end of September. (a) What was the annualized return of Fidelity Low Price Stock Fund? If I only invested in the first 6 months, what was the annualized return of the fund? At the beginning of 2017,I invested $1,000 in the fund. But I beginning of April, and then added back the $500 into the fund at the beginning of October. What was my account value at the beginning of October? What was my annualized return? Comparing with the annualized return in the first part of (a), why are they so different? (b) redeemed $500 from the Fund at the (c) Set up the equation to compute my dollar weighted annual return in (b)? Does there exist a dollar weighted return? If yes, what is it? If not, why not? (d) What was my time weighted annual return in (b)? (e) IfI did exactly the opposite as in (b), what was my total investment value at the beginning of October 2017? What can you say about market timing? (f) What was my dollar weighted annual return in (e)?

Explanation / Answer

.1 .(a)Beginning of month

Price

January,2017

$45.50

April,2017

$47.80

July,2017

$49.60

October,2017

$52.00

January,2018

$56.90

Dividend paid at the end of September ,2017=$4

Calculation Annualized Return :

Total Ending value in one year=$56.90+$4=$60.90

Beginning Value=$45.50

Annualized return=(60.90-45.50)/45.50=0.34

Annualized Return in terms of percentage-34%

Ending Value after 6 months=$49.60

Return in 6 months=(49.60-45.50)=$4.10

Percentage return in 6 months=(4.10/45.50)*100=9.01%

Annualized return=9.01*2=18.02%

.(b)Number of units at the beginning with $1000 investment=1000/45.50=21.9780

Price at the beginning of April=$47.80

Number of units redeemed=500/47.80=10.4603

Number of units balance=(21.9780-10.4603)=11.5177

Number of units added in October =500/52=9.6154

Total units available in October=11.5177+9.6154=21.1331

Total available units at beginning of January 2018, =21.1331

No dividend is received.

Value at the end of one year=21.1331*56.90=$1202.47

Value at the beginning of the year=$1000

Hence annualized return=(1202.47-1000)/1000=0.2025

Annualized Return in percentage=20.25%

Annualized return is different because:

.(c)Dollar weighted rate of return is internal rate of return ,rate of return at which Net Present Value of cash flow=Zero

Month

Cashflow

($1,000)

$500

($500)

$1,202.47

Assume dollar weighted rate of monthly return =r

The Equation to calculated monthly return r:

500/((1+r)^3)+1202/((1+r)^12)=1000+500/((1+r)^9)

Dollar weighted annual return=r*12

.(d)Time Weighted annual return:

Month

Cashflow

Value

January

($1,000)

$1,000

April

$500

$550.55

(11.5177*47.80)

July

($500)

1098.9204

(21.1331*52.00)

Jan-18

$1,202.47

First 3 months return =((550.55+500)/1000)-1=0.0505

Next 3 months return=((11.5177*52.00)/550.55)-1=0.0879

Next 6months return=(1202.47/1098.9204)-1=0.0942

Average Return for first six months=((1+0.0505)*(1+0.0878))-1=0.1428

Return for last six months=0.0942

Time weighted annual return=(1.1428*1.0942)-1=0.2505

Time weighted annual return in percentage=25.05%