The following table lists the month-end prices from May 2017 to July 2018 of the Spider S&P 500 Index ETF (SPY) and iShares 20+ Treasury Bond ETF (TLT), respectively. During this time period the average annual yield for the one-month Treasury bills is 1.292% or 0.1077% per month. Apply the following equation to calculate the monthly returns from June 2017 to July 2018 for SPY and TLT, respectively.

The monthly return for month n:

r_n = (Current month-end price Previous month-end price) / Previous month-end price =

(P_n P_n-1) / P_n-1

Monthly Returns Data

Date	Adj Close Price Pn: SPY	Adj Close Price Pn: TLT
5/31/2017	235.858	120.4887
6/30/2017	237.3616	121.4428
7/31/2017	242.2404	120.6433
8/31/2017	242.9471	124.7557
9/29/2017	247.8424	121.8577
10/31/2017	253.6826	121.8107
11/30/2017	261.4366	122.716
12/29/2017	264.6073	124.9404
1/31/2018	279.5203	120.8728
2/28/2018	269.3568	117.1966
3/29/2018	261.9736	120.548
4/30/2018	263.3276	118.0308
5/31/2018	269.7288	120.3966
6/29/2018	271.28	121.1741
7/31/2018	281.33	119.433

Using the monthly returns, find the values of the following inferences about SPY and TLT, respectively.

1. AAR
2. GAR
3. HPR
4. Standard deviation
5. Sharpe ratio
6. VaR (1%) and Var (5%)

1-Month 1-Month SPY T-bill T-bill SPY TLT SPY TLT TLT Monthly Monthly Adj Close Adj Close Monthly Price Annual Price Return Return Return Yield (%) Date Month P P Year 1r 1r r 5/31/2017 235.858 120.4887 6/30/2017 237.3616 121.4428 2017 Jun 0.6355% 0.7887% 0.82 0.000683 7/31/2017 242.2404 120.6433 2017 Jul 2.0346% -0.6605% 0.96 0.0008 8/31/2017 242.9471 124.7557 2017 Aug 0.2913% 3.3519% 1 0.000833 2017 Sep 9/29/2017 247.8424 121.8577 1.9949% -2.3503% 0.96 0.0008 10/31/2017 253.6826 121.8107 0.95 0.000792 2017 Oct 2.3291% 0.0385% 11/30/2017 261.4366 122.716 2017 Nov 3.0108% 0.7404% 1.06 0.000883 12/29/2017 264.6073 124.9404 2017 Dec 1.2055% 1.7964% 1.14 0.00095 1/31/2018 279.5203 120.8728 2018 Jan 5.4828% -3.3097% 1.29 0.001075 2/28/2018 269.3568 117.1966 2018 Feb 1.41 0.001175 -3.7038% -3.0886% 3/29/2018 261.9736 -2.7793% 2.8195% 120.548 2018 Mar 1.5 0.00125 4/30/2018 263.3276 118.0308 2018 Apr 1.68 0.5155% -2.1102% 0.0014 5/31/2018 269.7288 120.3966 2018 May 1.68 2.4018% 1.9846% 0.0014 6/29/2018 7/31/2018 271.28 121.1741 2018 Jun 0.5734% 0.6437% 1.74 0.00145 2018 Jul 281.33 119.433 3.6377% -1.4473% 1.9 0.001583 GAR AAR HPR St Dev Sharpe VaR (1%) VaR(5%) 1-Month 1-Month SPY T-bill T-bill SPY TLT SPY TLT TLT Monthly Monthly Adj Close Adj Close Monthly Price Annual Price Return Return Return Yield (%) Date Month P P Year 1r 1r r 5/31/2017 235.858 120.4887 6/30/2017 237.3616 121.4428 2017 Jun 0.6355% 0.7887% 0.82 0.000683 7/31/2017 242.2404 120.6433 2017 Jul 2.0346% -0.6605% 0.96 0.0008 8/31/2017 242.9471 124.7557 2017 Aug 0.2913% 3.3519% 1 0.000833 2017 Sep 9/29/2017 247.8424 121.8577 1.9949% -2.3503% 0.96 0.0008 10/31/2017 253.6826 121.8107 0.95 0.000792 2017 Oct 2.3291% 0.0385% 11/30/2017 261.4366 122.716 2017 Nov 3.0108% 0.7404% 1.06 0.000883 12/29/2017 264.6073 124.9404 2017 Dec 1.2055% 1.7964% 1.14 0.00095 1/31/2018 279.5203 120.8728 2018 Jan 5.4828% -3.3097% 1.29 0.001075 2/28/2018 269.3568 117.1966 2018 Feb 1.41 0.001175 -3.7038% -3.0886% 3/29/2018 261.9736 -2.7793% 2.8195% 120.548 2018 Mar 1.5 0.00125 4/30/2018 263.3276 118.0308 2018 Apr 1.68 0.5155% -2.1102% 0.0014 5/31/2018 269.7288 120.3966 2018 May 1.68 2.4018% 1.9846% 0.0014 6/29/2018 7/31/2018 271.28 121.1741 2018 Jun 0.5734% 0.6437% 1.74 0.00145 2018 Jul 281.33 119.433 3.6377% -1.4473% 1.9 0.001583 GAR AAR HPR St Dev Sharpe VaR (1%) VaR(5%)