ETF
After researching ETF funds, an investor learns that out of 10,000 ETFs, 1,000 outperform S&P500 and 9000 do not. A research analysis has a track record with accuracy of 70% (analysis says buy when ETF outperforms, don't buy when ETF underperforms).
Without having an access to the research analysis, what is the probability that the investor chooses an ETF that outperforms?
Without having an access to the research analysis, what is the probability that the investor chooses an ETF that underperforms?
What is the probability that research analysis will recommend an ETF as a buy?
What is the probability that research analysis will recommend an ETF as a do-not-buy?
What is the probability that an investor invests in an outperform ETF if the research analysis says buy?
What is the probability that an investor invests in an undeperform ETF if the research analysis says do not buy?
What ca
n you conclude about the value of the research analysis (i.e. how much is it worth compare to just choosing an ETF randomly)?
Housing
A company must decide whether to leave its model homes unfurnished, furnished with minimal accessories, or completely furnish them using a custom decorator. The result of the decision is affected on the condition of the housing market. The following is the payoff table:
They have an internal forecaster who thinks that:
P(weak)=0.2
P(moderate)=0.4
P(strong)=0.3
P(very strong)=0.1
They also consider to hire a consultant who to conduct economic forecasting for improving the probability estimate. Based on his past experience, these are his predictions:
P(economy rise|weak market)=0.4
P(economy rise|moderate market)=0.7
P(economy rise|strong market)=0.8
P(economy rise|very strong market)=1
P(economy down|weak market)=0.6
P(economy down|moderate market)=0.3
P(economy down |strong market)=0.2
P(economy down |very strong market)=0
Calculate the payoff and determine the decision the company should make using each of the decision making under certainty criterion
Calculate the payoff and determine the decision the company should make using the decision making under risk criterion. What is the EVPI?
Calculate the payoff and determine the decision the company should make using the decision making under risk uncertainty criterion. How much is the maximum amount they should pay the consultant? What is the efficiency?
Survey
SurveyGood is a survey company collecting data from customers. Over years, they have the following response rate in percent:
Draw the time series chart. Verify with regression that using a stationary model is appropriate. State the p-value as well.
Forecast the future period using each of the these stationary models: last period, simple MA with 3 periods, weighted MA with 3 periods and weight of 0.5,0.3,0.2.
Forecast the future using the exponential smoothing model. By minimizing the MSE, find the optimum value of alpha and its corresponding forecast.
Based on MSE of models you have done, which one models gives the most accurate forecast?
Following the previous data collection, they got another 10-period data. John the CEO thinks that business is getting better because they get more responses.
Verify with graph and regression if there really is an uptrend. State the p-value as well.
Using the linear regression method, what is the forecast for period 12?
By minimizing MSE, find the optimal smoothing parameters for the Holt's model of this data.
Using the Holt's model, what is the forecast for period 13?
John observes the data and believes that there is a seasonal factor of 2. Verify this using classical decomposition and verify it (hint: use MSE value).
Calculate the adjusted seasonal factors.