# Mathematics Question

##
Description

## Having Trouble Meeting Your Deadline?

Get your assignment on** Mathematics Question ** completed on time. avoid delay and – **ORDER NOW**

Please calculate the historic decile statistics: I have attached the excel sheet which needs to be filled out

i. average return (remember to divide the average by 100 to convert to decimal)

ii. variance

iii. standard deviation

iv. compound return

In the excel sheet comment on your findings. What do you find? How do small firms perform relative to large firms?

The Geometric (Time-Weighted) Average Return

The arithmetic average provides an unbiased estimate of the expected future return. But what does the time series tell us about the actual

performance of a portfolio over the past sample period? Let’s continue @ Example 5.4 using its very short sample period just to

illustrate. We will present results for meaningful sample periods later in the chapter.

Column F in I Spreadsheet 5.2 shows the investor’s “wealth index” from investing Sl in the portfolio at the beginning of the Page 132

first year. Wealth in each year increases by the “gross return.” that is. by the multiple (1 + HPR), shown in column E. The

wealth index is the cumulative value of Sl invested at the beginning of the sample period. The value of the wealth index at the end of the

fifth ver. $1.0275. is the terminal value of the Sl investment, which implies a 5-vear cumulative return of 2.75%.

An intuitive measure of performance over the sample period is the (fixed) annual HPR that would compound to the same terminal value

resulting from the sequence of actual returns in the time series. This is called the geometric or compound rate of return. Denote the

geometric rate by g, so that

Terminal value = (1 + r1) X (1 + 72) x -. X (1 + rs) = 1.0275

(1 + g)” = Terminal value = 1.0275 (cell F6 in Spreadsheet 5.2)

8 = Terminal value!

– 1 = 1.02751/5

(5.14)

Practitioners often call g a time-weighted (as opposed to dollar-weighted) average return to emphasize that each past return receives an

equal weight in the process of averaging. This distinction can be important because investment managers may experience significant

changes in funds under management as investors purchase or redeem shares. Rates of return obtained during periods when the fund is

large have a greater impact on Anal value than rates obtained when the fund is small. We discuss this distinction in @ Chapter 24 on

portfolio performance evaluation.

Notice that the geometric average return in L Spreadsheet 5.2, 54%, is less than the arithmetic average, 2.1%. The greater the volatility

in rates of return, the greater the difference between arithmetic and geometric averages. If returns come from a normal distribution, the

expected difference is exactly half the variance of the distribution, that is,

E (Geometric average) = E [Arithmetic average| – 1/20?

(5.15)

(A warning: I use @ Equation 5.15, you must express returns as decimals, not percentages.) When returns are approximately normal.

[ Equation 5.15 will be a good approximation.

Page 133

The discrepancy between the geometric and arithmetic averages arises from the asymmetric effect of positive and negative rates of

returns on the terminal value of the portfolio. (4 Example 5.5 illustrates this effect.

**Explanation & Answer**

Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Order Now and we will direct you to our Order Page at Litessays. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.

Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.