# Modern portfolio theory (mpt) | Business & Finance homework help

EXERCISE 4

Creating a hyperbola:

One of the salient features of Modern Portfolio Theory (MPT) is the phenomenon of putting two

stocks together such that the resulting portfolio has a lower standard deviation (lower risk) than

either of the component stocks. This is the magic of diversification and this exercise illustrates

the phenomenon graphically.

1) Overview: Given the pps data of two firms* from your portfolio file of last week you will use

Excel to create the hyperbola that would result from plotting the risk/return profile of a set of five

portfolios, each comprised of the two stocks as the dollar mix goes from 100% of the dollars in

stock A and 0% in stock B, to 0% in Stock A and 100% in stock B.

* Note: For Spring 2014, stock A= GE & stock B=GOOG.

2) You will begin by generating data for these five portfolios. The data will be risk and return,

where risk is the standard deviation (population) of the daily returns of the portfolio and returns is

the total annual (or 12 month) return.

3) The dollar mix of the five portfolios that you plot will be:

Portfolio 1: 100% stock A and 0% stock B

Portfolio 2: 75% stock A and 25% stock B

Portfolio 3: 50% stock A and 50% stock B

Portfolio 4: 25% stock A and 75% stock B

Portfolio 5: 0% stock A and 100% stock B

4) Start by creating 5 separate portfolios in a new sheet (or “tab”) [Rename the tab “hyperbola”]

in your portfolio file with the two firms mentioned above (stockA and stockB). Each of the five

new portfolios will have the three tiers (pps, mkt value, daily returns) and each portfolio will have

three columns (the total portfolio, stockA , stockB). There will be a total of 15 new columns.

See also the screenshot called “hyperbola snapshot” available on the Moodle webpage.

5) Populate tier1 of stock A and stock B with the original pps data found in sheet1. Do this five

times, that is, once for each of the five portfolios.

6) Calculate the “normalized number of shares” for stockA and stockB using =10000/ average

pps . Enter “number of share” data for both stocks in each of the five portfolios such that

portfolio1 has 100% of the normalized number of shares for stockA and 0% of the normalized

number of shares for stockB. Portfolio2 has a 75% and 25% mix, and so on for the other three

portfolios.

7) Using the same logic and formulas as in the main sheet, calculate the Market Values (Tier2)

and Daily Returns (Tier3) for all 5 portfolios in the hyperbola tab.

8) Calculate the Standard Deviation (of the population using =STDEVP ) of the Daily Returns of

each of the 5 portfolios. Put these in a row below tier 3.

9) Calculate the Total Return (top to bottom of Tier2) for each of the 5 portfolios using (last dayfirst day)/first day. Put these in a row below the STDEVP.

10) Build and new little block of data (see again “hyperbola snapshot”) in which you display the

std deviations and total returns of the five portfolios. For each of the cells you can simply

reference the appropriate cell above. For example, use “=B766” [I’m don’t the actual row

number] to display “.01857” as calculated in a previous cell.

11) Chart the stdevp and totalK of the 5 portfolios. Use “scatter with data points connected by

smooth lines”.

12) Optional: Modify the two axis so as to exaggerate the curve. Chart Tools>Layout >Axis.

That is, by moving the borders closer to the actual curve, the curve will become more

pronounced.