Risk+-+mean,+variance,+standard+deviation,+risk+aversion,+risk+neutral,+risk++lover,+optimal+search


 * Risk: mean, variance, standard deviation,** **risk aversion, risk neutral, risk lover, optimal search**
 * By: Carrie Pickering**

Risk is a part of everyday life. From making purchases to driving to work risk is inherent in everything we do. Even worldwide markets are based upon minimizing risk as the value of the dollar goes down. (Platt, 2007) Some say the dollar decreasing in value is based upon the credit crisis caused by sub-prime mortgages. (Raymond, 2007) A lack of meaningful information on the part of buyers and their subsequent risk-taking has lead to the melt-down and credit crunch in the housing industry in late 2007.

Based upon personality, characteristics, and culture some people are more open to taking risks and dealing with uncertainty while others are more prone to being conservative. Why is this? There are three ways to describe uncertainty and the behavior of consumers and business:

Rather than make a risky decision with unsure profits or consequences, a decision is made that has a lower risk of failing and is a “sure thing” for profit or benefits. (Baye, 2006) Examples: Honda Odyssey, a good family car Car insurance or home owner’s insurance
 * __Risk Averse:__**

Decisions and actions are made based upon maximizing expected profits or benefits. The potential variation in profits or benefits is not considered. Risk neutral essentially means indifferent to risk. (Baye, 2006) Example: Toyota Camry, popular, quality product Remodeling a kitchen for maximum resale value
 * __Risk Neutral:__**

Prefers risky decisions or actions with unsure, potentially higher gains, than the “sure thing”. (Baye, 2006) Example: Porsche, sleek, fast, fun Taking a position with no salary and only commission
 * __Risk Lover:__**

Consumers and businesses can move between the different types of risk taking depending upon the situation. Businesses attempt to anticipate the reactions of consumers and thus put into place procedures, advertising campaigns, and quality regulations to induce even the most risk averse consumers to purchase goods. But how does a business or consumer search for a good or come to a decision with others in the market working against them?

__**Optimal Search Rule:**__ Let’s look at the Search Rule. This optimal search rule means that products and projects (really anything) and its corresponding price is rejected above a certain point called the reservation price. The reservation price is the point at which consumers are indifferent between buying or continuing to search. When the price of a good is above the reservation price consumers stop looking and when it is below they continue to look. The optimal search strategy can be represented in an equation as well as graph form.

**EB(R) = c when**
EB expected benefits R reservation price c cost per search

__**Mean, Variance, Standard Deviation:**__ Risk in essence can be categorized by the amount of information that is available about a given product or situation. But how do you know that the information you have is valuable or meaningless? One way to find if the information available in the market is valuable or meaningless is by conducting a statistical analysis. Statistics give information about the degree of risk as well as the variables or unknowns. Some of the most common statistics run on data are mean, standard deviation and variance. If you have ever had a statistics class these terms should sound very familiar to you. If you need a refresher or more information on statistics and regression analysis please follow this link. Regression Analysis

__**Mean:**__ The mean or "average" is a common statistic that many people do not even realize is actually a statistic. The mean or average is used everyday by people in different industries around the world. The mean takes into account all data and sample data. To calculate the mean in statistics you simply add all values and divide by the amount of values. For example you have three values, 5, 6, and 7. You add and get the number 18. Then you divide by the amount of values 3. The mean is 8. This seems wonderful, but the mean can be skewed quite easily by data that is extreme called outliers.(Doane and Seward, 2007) To calculate the mean in economics is slightly different. According to Baye, to calculate the mean in economics a weighted mean is used. This simply gives a weight or probability to each value that is used. It is computed as the sum of the probabilities that different outcomes will occur multiplied by the resulting payoffs. You can use the following equation:

//E[x] = q1 x1 + q2 x2 +…+ qn xn//
xi is payoff i qi is the probability that payoff i occurs q1 + q2 + ........qn = 1

__**Variance:**__ Variance plays a key role when calculating mathematical statistics. Unfortunately, for most people looking at the result of the calculated variance is not an intuitive process. Meaning, that unless you know what you are looking at it doesn't seem important or relevant. (Doane and Seward, 2007) Variance measures how much the data varies. Makes sense right? Because it indicates how much or how little values vary, this is a very important way to analyze data. In economics variance is a measure of risk. You can use the following equation to calculate variance:

//**s**//**2 = q1 (x1- //E[x]//)2 + q2 (x2- //E[x]//)2 +…+qn(xn- //E[x]//)2** The sum of the probabilities that different outcomes will occur multiplied by the squared deviations from the mean of the variable.

__**Standard Deviation:**__ The standard deviation is a number that helps to understand how values in a data set vary from the mean. The standard deviation is simply the square root of the variance. By taking the square root the units in which the data are measured, for example dollars, miles, pounds, ounces) all of the units of measurement become the same as the variable X.

__**Multiple Choice Questions:**__

Q1. What would be considered a risk-averse action? a. Baking a new recipe for the family Christmas party when your mother-in-law is picky about her cakes. b. Going out on a limb and buying an expensive present that you are unsure the person will like. c. Giving a gift card to your niece who is a snotty teenager. d. Wearing a revealing and sexy outfit when meeting your future in-laws for the first time.

Q2. Using the previous question which could be considered a risk-neutral action? a. A and B b. D and B c. D only d. none of the above

Q3. You missed Black Friday, the best day of the year to go shopping. However you truly want to purchase a Wii for you and your husband. In the Optimal Search Rule when the price of the Wii is above the price you are willing to pay? a. Stop searching. b. Increase budget. c. Look for sales and discounts. d. Recruit friends to help you find it at your reservation price.

Q4. In economics, how is calculating the mean different than in statistics? a. It is not different. b. Outlying data does not effect it. c. The probability of resulting pay offs is used in the equation.

Q5. Standard deviation helps you to understand how data.......**.** a. uses measurements such as dollars, pounds and ounces. b. varies from the mean. c. is the square root of the variance. d. is calculated.

__**Answers:**__

Q1.The answer is C. Risk aversion deals with making decisions that have low risk and are a "sure thing". Teens can be very critical of horrible presents. The safe way is to let your niece pick her present with the gift card.

Q2.The answer is D. All of the actions A,B, and D are risky and have potentially high rewards. There is no neutral choice that allows a maximum amount of benefit.

Q3.The answer is A. Wii's are very popular and you may in fact increase your budget or even recruit friends. However in the strictest economic sense of optimal search you will not continue to search for a Wii.

Q4.Than answer is C. To calculate the mean in economics is slightly different. To calculate the means in economics is computed as the sum of the probabilities that different outcomes will occur multiplied by the resulting payoffs.

Q5.The answer is B. The word standard deviation explains it self, i.e. deviation. Standard deviation tells how much the data varies from the mean.

__**References:**__

Baye, Michael R., //"Managerial Economics and Business Strategy"//, __McGraw-Hill Irwin__, 2006.

Doane, David P., Seward, Lori E., //"Applied Statistics in Business and Economics"//, __McGraw-Hill Irwin__, 2007.

Platt, Gordan, //"As Global Markets Stabilize, Analysts Say Dollar Could Lose Appeal As Safe-Haven Currency//", Global Finance; October 2007, Vol. 21 Issue 9, p115-120.

Raymond, Maureen, //"The Perfect Storm?"//, Accountancy; October 2007, Vol. 140 Issue 1370, p105-105.