Stock Opening Closing Number of Calculate Calculate the Calculate the Time Retur

Question

Stock Opening Closing Number of Calculate Calculate the Calculate the Time Return Price Price Days the the Annual Stock was Holding Retrn Continuous Period(assume Return compounded Equivalent and repeated for the whole year) 9$220$22 C 350$345 $57 $60 A 20 I 5222 4 4 4 Suppose you have the following stocks (A, B, and C) and their respective purchasing price and closing (sell) price. Calculate the HPR, Annual Return, and Continuous Time Equivalent Return. (Please show formulas used, and if possible, how to enter the data in excel. Thank youl)

Explanation / Answer

Let's take it by one by one.

1) HPR: Assuming no dividend was given, then the formula would become

HPR=(final Investment value-Initial Value investment)/Initial investment value

Stock A

=(60-57)/57= 5.26%

StockB

=(222-220)/220=2/220=0.909%

Stock C;

=(345-350)/350=-5/350= -1.43%

HPR for the stock Portfolio:

=(1+return on stock A)*(1+retutn on stockB)*(1+retturn on stockC)-1

=(1+0.0526)*(1+0.00909)*(1-0.0143)-1=1.0469-1=0.0469=4.69%

2) Annual Return:

Annualized HPR = {[(Income + (End of Period Value – Initial Value)] / Initial Value+ 1}1/t – 1, where t = number of years.

Putting the values in the above equation we get:

Stock A:

AHPR=[(60-57)/57+1]^(365/4)-1=107.53-1=106.53*100=10653%

Note that we have taken (365/4), as it is mentioned that 4 day period is compounded continuously for the year.

StockB:

AHPR=[(222-220/220)+1]^(365/4)-1=2.2835-1=1.2835*100=128.35%

StockC:

AHPR=[(345-350)/350+1]^(365/4)-1=1.9857-1=0.9857*100=98.57%

3) Continuous Time Equivalent Return:

StockA

CTER=e^(rt)=natural log(annualized rate of return)

=ln(106.53)=4.6684*100=466.84%

StockB

CTER=e^(rt)=natural log(annualized rate of return)

=ln(1.2835)=0.2496*100=24.96%

StockC

CTER=e^(rt)=natural log(annualized rate of return)

=ln(0.9857)=-.0144*100=-1.44%

Hope above clarifies everything, if any doubts please feel free to ask.

Best of Luck!

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