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## Investment in CD and Stocks

Investing in CD, the interests are defined by contracts. Only the reliabilities of banks are uncertain. Investing in stocks, in addition to reliabilities of companies, their future stock rates are uncertain, too. The predicted stock rates are defined by a coefficient that shows the relation between the present and the predicted stock rates. The prediction "horizon" is supposed to be the same as the maturity time of CD.

To simplify the model suppose that one predicts different values of relative stock rates with corresponding estimated probabilities
.
In this case, one may define probabilities of discrete values of wealth by exact expressions. The expressions for CD remains the same. Therefore, we shall consider only stocks assuming that and . Then

|  |  | (10)

Here
. The reliabilities , the stock rate predictions and their estimated probabilities are defined by experts, possibly, with the help of time series models such as ARMA For example, maximal values of multi-step prediction are considered as "optimistic" estimates. The minimal values- as "pessimistic" ones. The average values of multi-step prediction are regarded as "realistic" estimates.

Here is a simplest illustration were and . In this case from (5) (10) the probabilities of wealth returns are

Here
.

Next: Optimal Portfolio, Special Cases Up: Expected Utility Previous: Investment in CD