I am still confused about this problem. Can you go in deeper detail on how to so

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I am still confused about this problem. Can you go in deeper detail on how to solve this problem?

1. (Geometric average rate of return: Long-run performance) The table below shows the performance of Fidelity Magellan Fund (FMAGX) and SPDR S&P 500 ETF Trust (SPY) for each full calendar year over the Period d 2008-2013 2008 2009 2010 2011 2012 2013 ar -49.40% 36.83% 1 1 .55% 1.96% FMAGX 41.13% 26.30% 12.41% 14.88% 17.99% 15.84% 35.30% 321 3% SPY (a) Calculate the geom (b) If the initial investment at the beginning of 2008 was $10,000, what was the market value of the investment (S) in FMAGX at the end of 2013? Calculate (c) If the initial investment at the beginning of 2008 was S10,000, what was the market value of the investment (S) in SPY at the end of 2013? Calculate the whole-period return(% (d) Which investment yields better performance over the whole period 2008-2013? (e) In part (a), calculate the performance differential (%) between FMAGX and SPY using SPY as benchmark. (f) In parts (b) and (c), lculate the performance differential (%) between FMAGX and SPY using SPY comme of return (annual; %) for both FMAGX and SPY ear rn Solutions: (a) Geometric average return of FMAGX (1-0.4940) (1+0.4113+1241) 0.55) (1+0.1799) +0.3530) (6 1.1 33485-(1%)''6 r,-1.13348541/6)-l-)r.* 2.11%, Noted Using a calculator, 1/6s0·166666667 then enter 1.1334850.166666667to get 1.133485 (1/6 1.021102.. ri-I . 1 3 348541 /6)-1 0.02 1 1-2. I 196 Geometric average return of SPY 1-0.3683)+0.2630) 1+0.1488)*1+0.0196) (1+0.1584) 1+0.3213) P6 1.430370-(1%)% re~ 6.15% (b) 10,000 * 1 . 1 33485-1 1 ,334.85; ( 1 1 ,334.85-10,000), 10,000-13.35% (c) 10,000* 1.430370 14.303.70; ( 14,303.70-10,000)/10,000-43,04 % (d) SPY (e) 2.11-6.154.04 FMAGX underperforms when using SPY as benchmark. (f) 13.35-43.04-29.69(%) over 6 years. Solving r, which is the geometric average rate of retu (W/Vo)=( 1 + re )"N·,-w(1 + ri ) "N (The ending value) Long-run (or buy-and-hold) return = (Vi-Vo)/Vo omparison A-capital or amount due, V-the principal amount, r the fixed annual interest rate At the end of the first year: A-V(1+r)

Explanation / Answer

(a) FMAGX Geometric Average Return (Rf) is calculated as given below:

(1+Rf)^(6) = (1+FMAGX 2008 Return) x (1+FMAGX 2009 Return) x ....................x (1+FMAGX 2013 Return) = (1-0.494) x (1+0.4413) x (1+0.1241) x (1-0.1155) x (1+0.1799) x (1+0.353)

Rf = (1.33485)^(1/6) - 1 = 1.02112 - 1 = 0.02112 or 2.11 % approximately

SYP Geometric Average Return(Rs) is calculated as given below:

(1+Rs)^(6) = (1-0.3683) x (1+0.263) x (1+0.1488) x (1+0.0196) x (1+0.1584) x (1+0.3213)

Rs = (1.430370)^(1/6) - 1 = 0.06147 or 6.15 % approximately.

NOTE: Geometric Average Return is the single equivalent return which would equalize the total return over a period of time to the combination of individual returns over the same time period.

(b) 6-year return on the FMAGX implies the total return over the aforementioned time period when an initial investment of $ 10000 is made in FMAGX.

Initial Wealth Value = $ 10000

Final Wealth Value = (1.0211)^(6) x 10000 = $ 11334.69 (Market Value of Investment after 6 Years)

Total Return over 6 Years = (11334.69 - 10000) / 10000 = 0.13346 or 13.35 % approximately.

(c) The whole period return is the same thing as the 6 years return asked in part (b).

Initial Wealth Value = $ 10000 and Final Wealth Value = (1.0615)^(6) x 10000 = $ 14306.058

Total Return over 6 Years = (14306.058 - 10000) / 10000 = 0.4306 or 43.06 % approximately.

(d) As the total return of SPY is greater than that of FMAGX, the former yields better returns than the latter.

(e) Performance Differential Calculation using part (a) calculation as benchmark implies comparing the geometric average return of SPY and FMAGX, with SPY functioning as the benchmark.

Performance Differential = FMAGX Geometric Average Return - SPY Geometrice Average Return = 2.11 - 6.15 = - 4.04 %

(f) Performance Differential Calculation using part (b) and (c) calculation as benchmark implies comparing the total returns of SPY and FMAGX, with SPY as the benchmark.

Performance Differential = FMAGX Total Return - SPY Total Return = 13.35 - 43.06 = - 29.71 % approximately,

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