Question

Teachers’ Retirement System of the City of New York offers several types of investments for its members. Among the choices are investments with fixed and variable rates of return. There are several categories of variable-return investments. The Diversified Equity Fund consists of investments that are primarily made in stocks, and the Stable-Value Fund consists of investments in corporate bonds and other types of lower-risk instruments. The data in TRSNYC represent the value of a unit of each type of variable-return investment at the beginning of each year from 1984 to 2015. (Data extracted from “Historical Data-Unit Values, Teachers’ Retirement System of the City of New York,” bit.ly/SESJF5.)

a.     For each time series, plot the data in a line graph.

b.     For the Diversified Fund, compute a linear trend forecasting equation.

c.     For the Diversified Fund, compute an exponential trend forecasting equation.

d.     For each of the models in parts b and c, forecast the unit value for 2016

e.     Which of the two forecasts do you believe is more accurate and why?

Year	Diversified Equity	Stable-Value
1984	13.111	10.342
1985	13.176	11.073
1986	16.526	11.925
1987	18.652	12.694
1988	15.564	13.352
1989	20.827	13.919
1990	24.738	14.557
1991	22.678	15.213
1992	28.549	15.883
1993	29.829	16.510
1994	32.199	16.970
1995	30.830	17.351
1996	39.644	17.682
1997	45.389	18.004
1998	54.882	18.341
1999	64.790	18.678
2000	74.220	18.962
2001	67.534	19.320
2002	57.709	19.673
2003	44.843	19.735
2004	55.993	19.609
2005	60.909	19.520
2006	63.038	19.452
2007	70.413	19.441
2008	71.460	19.493
2009	42.493	19.496
2010	52.629	19.374
2011	58.207	19.223
2012	55.630	19.470
2013	62.174	19.382
2014	77.656	19.039
2015	81.363	18.311

Answer 1

In the picture given below in the table in excel sheet t denotes year and Y denotes Diversified equity.

-406.4361 -382.1841 446.2729 466.3625 358523 437.4 441 470 361 -385.5 285 428.2 225 -387.8 169 -354.2 121 277.581 277.5 49 226925 31 21984 3 1985 4 1386 5 1987 13.176 16.526 18.652 15.560 20.827 24 738 22 678 28.549 29.829 32.199 30.83 39644 15.308 54. 882 64. T9 74.32 67.534 71983 81990 g139 0 1992 111993 3 1994 3 3 1995 14 1996 15 199T 6 1938 17 195Ss 18 2000 19 2001 202002 21 2003 13 -64.731 202.6 288.55 25 li 313.9 mim 49: lili 503 9481 5T.703 44.843 55.933 60.S09 63.038 70.413 71.46 42 493 52.629 58.207 55.63 62.174 77.656 81.363 22 2004 23 2005 24 2006 25 2007 26 2008 27 2003 28 2010 B70 819.49163 1056.2225 1214.8 289 807.37361 1105.21 441 1338.8 350.8 625 678 7 729 2252:841 25223961 i3 10 10 29 2011 302012 31 : 2013 32 2014 33 2015

Diversified Equity 90 70 60 50 30 20 10 o O

We shift th e onigio iz. 199g and 2 2000 Let the lin ec equity) and a be i Σχ so. a and b are estimated by 32 -10705. 28-0. 981056 yと 10912 2. Hence lineorr tren

d) forcasting value 2016 Lineon trend equalions we bave yt- 4S. 864 2 2 + 0.981056 2e wben t= 2016 i-we-get-from-a χ= 2(2016-1999:S) Hence dives sified eacity -or 2016 is oS6 x 33 y 20 78 . 23906