MisterNs magic formula explained
Here comes the big formula: File:7216 0.png It attempts to explain the price File:7216 2.png) an individual should be willing to pay for any asset. He or she should buy the asset until the market price is as high as his individual price. File:7216 3.png is the expected value of File:7216 4.png File:7216 5.png Assumptions are:
There are only two time periods (File:7216 6.png and File:7216 7.png).
- The asset is completely paid out in File:7216 8.png , the pay-out is File:7216 9.png . - The investors sole goal is maximising the combined utilities of consumption in File:7216 10.png File:7216 11.png File:7216 12.png. - File:7216 13.png is differentiable in the relevant area. - Consumption is affected by the purchase of the asset: File:7216 14.png File:7216 15.png , where File:7216 16.png is the amount of the asset the investor chooses to purchase and File:7216 17.png is the consumption the investor would enjoy had he not purchased any of the asset.
Typically, for a risk-averse investor, File:7216 18.png is a convex, strictly increasing function like File:7216 19.png or File:7216 20.png.
One can rewrite the basic formula to another, perhaps somewhat clearer form:
File:7216 1.png (Where File:7216 21.png is the covariance.)
I will not delve deeper into that now.
