A fund's risk appetite is such that it wants to be 90% certain that it will not lose more than 20% in any one year. Using the performance of the S&P 500 between 1970 and 2021 (see Table 24.1), determine the beta the fund should have. Assume a risk‐free rate of 3% per annum. 

Table 24.1

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Year Return (%) 1970 1971 4.01 14.31 1972 18.98 1973 -14.66 1974 -26.47 1975 37.20 1976 23.84 1977 -7.18 1978 6.56 1979 18.44 1980 32.50 1981 -4.92 1982 21.55 1983 22.56 1984 6.27 1985 31.73 1986 18.67 1987 5.25 Year Return (%) 1988 16.61 1989 31.69 1990 -3.10 1991 30.47 1992 7.62 1993 10.08 1994 1.32 1995 37.58 1996 22.96 1997 33.36 1998 28.58 21.04 -9.10 -11.89 -22.10 28.68 10.88 4.91 1999 2000 2001 2002 2003 2004 2005 Year Return (%) 2006 15.79 2007 5.49 2008 -37.00 26.46 15.06 2.11 16.00 2009 2010 2011 2012 2013 32.39 2014 13.69 2015 1.38 2016 11.96 2017 21.83 2018 -4.38 2019 31.46 2020 18.40 2021 28.71