Question

1. Table 3 (below) shows annual returns for the S&P 500 for the years 2000-2016:

Table 3: Annual Returns

Year	Returns
2000	-9.0%
2001	-11.9%
2002	-22.0%
2003	28.4%
2004	10.7%
2005	4.8%
2006	15.6%
2007	5.5%
2008	-36.6%
2009	25.9%
2010	14.8%
2011	2.1%
2012	15.9%
2013	32.2%
2014	13.5%
2015	1.4%
2016	11.7%

Calculate:

1. The cumulative return over the 17 years;
2. The average annual return;
3. The standard deviation;
4. The Sharpe Ratio (assuming a risk free rate of 2.3% on average)

Answer 1

Solution:

• Cumulative Return : (Current Stock Value- Purchase Value) / Purchase Value * 100%

= (209.3536916-100)/100 * 100%

= 109.35%

Suppose, we purchase a stock at the beginning of for $100. Then stock value at the end of 2016 is = 209.3536916

• Average Annual Return = Sum of all the return for 17 years / No. of Years

= 103/17

= 6.06%

• Standard Deviation =

=

= 71.72740882

• Sharpe Ratio:

For Return of Portfolio either we can use Average return of of the portfolio over the years or else we can take the current one also considering the current conditions of the market.

- Using Average Return =

= 0.052404

- Using Current Rate =

= 0.131052