Calculate the Sentiment Function (please show step by step how to do it, thank you).

These are the steps the professor wants us to follow:

1. Use the asset pricing equation to estimate Arrow-Debreu asset prices. The asset pricing equation for the case of RDU is v_k = w_k/g_k, where w_k are the RDU wights. For the case of Bayes the asset pricing equation is v_k = P_k/g_k, where P_k are the probabilities calculated according to Bayes. Remember that g_k = 1.2 under the strong regime and g_k = 0.95 in the weak regime

2. Calculate relative prices under RDU and Bayes

3. Calculate the log-difference of relative prices

4. Plot the value of the signal (0, 1, 2, 3, 4, 5, 6) agaisnt the log-difference of relative prices. This gives the sentiment function below.

 

Number of Ups 0 1 2 3 4 5 6 Number of Ups 0 1 2 3 4 5 6 RDU Strong Regime (Weight of each state) (Weight of each state) 0.049% 0.060% 1.240% 6.320% 16.970% 6.780% 1.930% Weak Regime Strong Regime (Price per state) 0.540% 4.250% 13.130% 30.830% 13.130% 4.250% 0.540% Weak Regime (Price per state) Number of Ups 0 1 2 3 4 5 6 Number of Ups 0 1 2 3 4 5 6 Bayes Strong Regime (Probability of each state) 0.050% 0.550% 2.740% 7.320% 10.970% 8.780% 2.930% Strong Regime (Price per state) Weak Regime (Probability of each state) 1.040% 6.250% 15.630% 20.830% 15.630% 6.250% 1.040% Weak Regime (Price per state) Number of Ups 0 1 2 3 4 5 6 RDU Relative Prices Bayes Log-difference Relative Prices