Question

the question is a mini case with 6 sub questions

Mini-Case After graduating from counting and finance, Jim dock ock raduating from college last spring with a major in ac- e and finance, Jim Hale took a job as an analyst trainee investment company in Chicago. His first few weeks e filled with a series of rotations throughout the firm's vari- cus operating un enerating units, but this week he was assigned to one of the firm's traders as an analyst. On his first day, Jim's boss called in in and told him that he wanted to do some rudimentary Salysis of the investment returns of a semiconductor manu- esturer called Advanced Micro Devices, Inc. (AMD). Specifi- cally, Jim was given the following month-end closing prices for the company spanning the period of November 1, 2011, through November 1. 2012: Date Closing Price 1-Nov-11 $5.69 1-Dec-11 5.4 3-Jan-126 .71 1-Feb-12 7.35 1-Mar-12 8.02 2-Apr-12 7.36 1-May-126 .08 Date 1-Jun-12 2-Jul-12 1-Aug-12 4-Sep-12 1-Oct-12 1-Nov-12 Closing Price $5.73 4.06 3.72 3.37 2.05 1.88 He was then instructed by his boss to complete the follow- ing tasks using the AMD price data (note that AMD paid no dividend during the period being analyzed). 5. Now calculate the compound annual rate of return using the geometric average monthly rate of retum Questions 1. Compute AMD's monthly realized rates of return for the entire year. 2. Calculate the average monthly rate of return for AMD us- ing both the arithmetic and the geometric averages. 3. Calculate the year-end price for AMD, computing the com- pound value of the beginning-of-year price of $5.69 per share for 12 months at the monthly geometric average rate of return calculated earlier: End-of-Year Beginning-of-Year Stock Price Stock Price Geometric Average 2 Monthly Rate of Return 4. Compute the annual rate of return for AMD using the be- ginning and ending stock prices for the period (i.e., 55.69 and $1.88). Compound Annual Geometric Average 2 Rate of Return Monthly Rate of Return 6. If you were given annual rate of return data for AMD's or any other company's stock and you were asked to esti- mate the average annual rate of return an investor would have earned over the sample period by holding the stock, would you use an arithmetic or a geometric average of the historical rates of return? Explain your response as if you were talking to a client who has had no formal training in finance or investments,

Answer 1

Solution for Q1

The realized rate of return = ((Share price at the end of the period/ share price at the start of the holding period)-1)*100

AMD's realized return for the month ended:

November 2011= ((5.4/5.69)-1)*100 = -5.10%, similarly,

December 2011 = 24.26%

January 2012 = 9.54%

February 2012 = 9.12 %

March 2012 = -8.23% 1.29352667

April 2012 = -17.39%

May 2012 = -5.76%

June 2012 = -29.14%

July 2012 = -8.37%

August 2012 = -9.41%

September 2012 = -39.17%

October 2012 = -8.29%

Solution for Q2

The arithmetic average monthly rate of return for AMD is the average of the 12 monthly realized return calculated above. The average is -7.33%

The formula for geometric average is [{(1+R1​)*(1+R2​)*(1+R3​)…*(1+Rn​)}^ (1/n)]​−1 , where r is the monthly realized returns as calculated in step 1 an n is the number of months.

plugging in those values, the geometric average is [{(1-0.051)*(1+0.2426)*....*(1-0.0829)} ^ (1/12)}]-1

=[{(0.33044) ^ (1/12) }- 1] *100 = -8.81%

Solution for Q3

Year-end price for AMD = $5.69 * (1-0.0881)^12 = $1.88 (formula is mentioned in the question)

Solution for Q4

During the year AMD's stock price went from $5.69 at the start of the year to $1.88 at the end. Hence the annual rate of return =[{($1.88/$5.69)-1}*100] = -66.96%

Solution for Q5

Compounded annual rate of return = [(1 + geometric average monthly rate of return)¹² -1]*100 = [(1-0.0881)¹²-1]*100 = - 66.96%

Solution for Q6

I would use the geometric average.

Let's say that the geometric annual average of a stock's return over 5 years is 10%. This means that on an average the stock grew was 10% from the stock price at the beginning of the year.

The arithmetic average does not capture that and is particularly not useful if there has been a lot of volatility. Let's say a stock grew 10% in the first year, 90% in the second slumped by 60% in the third, grew 5% in the fourth and fell 20% in the fifth, the average annual arithmetical return would be the average would be 5%, which is solid.

However, that did not give the full picture. The average annual geometric return for the stock is -6.82%, which gives a much better idea of the damage that the 60% decline in year 3 did. It means that on an average the stock kept falling by -6.82% each year