6. (20 points) It is well-known that investors tilt their portfolios based on forecast about the macroeconomy. In this question, I ask you to follow a similar strategy. Specifi- cally, I ask you to construct portfolio weights depending on the business cycle. Use the data on Wilshire 5000 and ICE BofA US Corporate Index value from Question 5. In addition, you need an estimate of macroeconomic conditions. Use the Smoothed U.S. Recession Probabilities computed by Federal Reserve Bank of St. Louis.4. This question guides you on how to do this. (a) First, we need to identify recessions and expansions. To do so, define a reces- sion whenever the recession probability is above 50%. Conversely, define an expansion whenever the recession probability is below 50%. For each state (i.e., recession and expansion), please calculate monthly mean returns and standard deviations for the equity and bond indices, as well as their correlation. (b) For each state, compute the monthly weights on equities and bonds in the tan- gency portfolio, using the formula from the slides. To compute tangency port- folio, use the following values for the risk-free rate in recession 0.53% and in expansion 0.35%. Note that you will have a different portfolio weight for equi- ties (bonds) in expansions and recessions. Please report these portfolio weights: equity Wrecession' wbonds and bonds Comment on these weights. expansions' recession' equity expansions (c) For each month, compute dynamic portfolio weights, defined as: equity Wt bonds = ,equity equity = Pr(recession)+ * wasion + (1 - Pr(recession)t) * Wexpansion bonds Pr(recession) * woondesion + (1 - Pr(recession)t) * Wexpansion Note that these weights w vequity and woods incorporate your views about the macroeconomic conditions via the recession probability Pr(recession)t. Please plot them as a function of time and describe them. When do you increase your risk exposure in equities? When do you decrease your risk exposure in equities? (d) What are the monthly expected return, standard deviation, and Sharpe ratio of the portfolio with the dynamic weights computed above? Convert expected return, standard deviation, and Sharpe ratio to an annual basis. Add this port- folio to the plot from Question 5 (h). Comment on the Sharpe ratio. Does this strategy achieve a higher Sharpe ratio than the tangency portfolio in Question 5? If so, why do you think this is the case? You can find these probabilities here: https://fred.stlouisfed.org/series/RECPROUSM156N. Please see the following paper on a way to compute these recession probabilities in real life: https://www.bundesbank.de/resource/blob/873254/f4886445179de330e2667ce625b9f6f1/mL/2021- 08-09-dkp-25-data.pdf