SIAM Journal on Financial Mathematics Assessment Answer

FFAVX is Fidelity advisor freedom 2005 fund the overall objective of the fund is to obtain high return along with the objective of preservation of principal as the fund will approach its date oftargetand beyond that. The fund has been designed for the investors who are about to reach retirement age and its target retirement age is 65. The fund is a combination of equity funds, short term funds, Bond funds and international equity funds.

FACFXis Fidelity advisor freedom 2010 fund the objective of Fidelity advisor freedom 2010 fund is similar to Fidelity advisor freedom 2005 fund the overall objective of the fund is to obtain high return along with the objective of preservation of principal as the fund will approach its date oftarget . The fund isa combinationof equity funds, short term funds, Bond funds and international equity funds.

VFINX the major objective of Vanguard 500 index fund investor share mutual fund is 2 continuously track the performance of given benchmark index which evaluates the investment return corresponding to high capitalization stocks. The fund is dominated by the stock of big United States companies and its major objective is to replicate the target index.

VBINX is Vanguard balanced index fund investor shares. The major objective of Vanguard balance index fund investor share mutual fund is divided into two categories. The first is with 60 of its asset the mutual fund evaluates the performance of the benchmark index and evaluates the return of United States equity Market. Whereas with the remaining 40 The fund evaluates the performance of given market-weighted bond index. The mutual fund includes investment in Mid Cap, large cap and small cap stocks. Apart from the equity with 40 of its assets the funds include corporate and Government Bonds.

VHCOX is Vanguard capital opportunity fund investor Share. The major objective of Vanguard capital opportunity fund investor shares to provide capital appreciation inlongterm. The fund majorlyinvestsin United States equity market and its focus is on the companies which have high earnings growth.

Part 2d

In thispartit can be observed that the beta of mutual funds when calculated with respect to Dow Jones index is slightly different from the beta of the mutual funds when calculated with respect to SampP 500 index. The difference between the calculated beta with respect to 2 benchmark indexes is due to the difference in the volatility of the index. All benchmark index have similar volatility but however, there isSlightdifference between the volatility of two indexes and the volatility of both the index is not exactly the same. Due to the difference in the volatility of both the indexes the calculated beta values of the Mutual Fund with respect to Dow Jone index and standard and poor 500 index is different.

Part 2E

Run TESTS /RUNS(MEDIAN)VFINX VBINX VHCOX FFAVX FACFX

/MISSING ANALYSIS.

Runs Test

VFINX VBINX VHCOX FFAVX FACFX

Test Valuea.0487 .0320 .0520 .0202 .0074

Cases lt Test Value 20 20 20 20 20

Cases gt Test Value 20 20 20 20 20

Total Cases 40 40 40 40 40

Number of Runs 24 22 18 22 23

Z .801 .160 -.801 .160 .481

Asymp. Sig. (2-tailed) .423 .873 .423 .873 .631

a. Median

Null HypothesisThe order of the return for VFINX is random.

Alternative HypothesisThe order of return for VFINX is not random.

With test value 0.0487, pgt5, I fail to reject null hypothesis and conclude that the order of the return for VFINX is random.

Null HypothesisThe order of the return for VBINX is random.

Alternative HypothesisThe order of return for VBINX is not random.

With test value .0320, pgt5, I fail to reject null hypothesis and conclude that the order of the return for VBINX is random

Null HypothesisThe order of the return for VHCOX is random.

Alternative HypothesisThe order of return for VHCOX is not random.

With test value .0520, pgt5, I fail to reject null hypothesis and conclude that the order of the return for VHCOX is random

Null HypothesisThe order of the return for FFAVX is random.

Alternative HypothesisThe order of return for FFAVX is not random.

With test value .0202, pgt5, I fail to reject null hypothesis and conclude that the order of the return for FFAVX is random

Null HypothesisThe order of the return for FACFX is random.

Alternative HypothesisThe order of return for FACFX is not random.

With test value .0074, pgt5, I fail to reject null hypothesis and conclude that the order of the return for FACFX is random.

Part 6

In this part we can observe that as per the geometric mean VHCOX ranks on top which is followed by VFINX. Similarly we can observe that as per the Sharpe ratiothe optimal portfolio ranks on top which is followed by 6 fund portfolio. Similarly on the basis of Treynor ratio also the optimal portfolio which is a mixture of risk free Assets and risky portfolio rhymes on top and it is followed by 6 fund portfolio

References

Schied, A., Speiser, L., amp Voloshchenko, I. (2018). Model-free portfolio theory and its functional master formula.SIAM Journal on Financial Mathematics,9(3), 1074-1101.

Runting, R. K., Beyer, H. L., Dujardin, Y., Lovelock, C. E., pyan, B. A., amp Rhodes, J. R. (2018). Reducing risk in reserve selection using Modern Portfolio Theory Coastal planning under sealevel rise.Journal of Applied Ecology,55(5), 2193-2203.

Platanakis, E., amp Urquhart, A. (2018). Should investors include bitcoin in their portfolios A portfolio theory approach.

Madan, D. B. (2018). Instantaneous portfolio theory.Quantitative Finance,18(8), 1345-1364.

Pal, S. (2018). Exponentially concave functions and high dimensional stochastic portfolio theory.Stochastic Processes and their Applications.

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