Risk premiums.

Hi all,

I need help solving a problem.

I have a risk premium of 2 % for a city called K. I also have the market size for that city (in number of people) and the number of days it takes to finish a deal.

I have 30 other cities. I have to find the risk premium for all these cities based on the 2 % for city K with the help of the knowledge I have of all the market sizes for each city and the days it takes to finish a deal.

SO what I want is to put a relation between the city K risk premium and the other cities. Let's say:

City K has a risk premium of 2%. The market size is 20 people and trading days of 40.
City B has a market size of 40 people and trading days of 10. The risk premium should be lower the bigger the market and the fewer the trading days.

How do I derive a risk premium for city B? I know that ratio: market size City B / Market size City K = 2 and that the trading days city B / trading days city K = 0.25.

Risk premium City B = Risk premium city K x ?

I have tried asking other economists but they dont know. Pleaase help me find a methodology!

I would really appreciate some help!

A first guess would be that your risk premium is related to your independent variables as a ratio some thing like this;
risk premium = parameter * trading days / market size

so the bigger the marker, the lower the risk premium
and as trading days decreases, the risk premium decrease

so for city K, the initial condition is
0.02 = parameter * 40 / 20

so your parameter is valued 0.01, and therefore for city B you have this;
city B = 0.01 * (0.25*40)/(2*20) = 0.0025

so the risk premium is .25% using that model

Obviously there could be some much more complicated relationship between those variates, and you would need more information to either suggest a model or test the fitted model.