A fund's risk appetite is such that it wants to be 97.5% certain it will not lose more than 25% 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 2.5% per annum.

Table 24.1

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Year Return (%) 1970 4.01 1971 14.31 1972 18.98 1973 -14.66 1974 -26.47 1975 1976 37.20 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 1999 21.04 2000 -9.10 2001 -11.89 2002 -22.10 2003 28.68 2004 10.88 2005 4.91 Year Return (%) 2006 15.79 2007 5.49 2008 -37.00 26.46 15.06 2.11 16.00 32.39 13.69 1.38 11.96 21.83 -4.38 31.46 18.40 28.71 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021