Market Risk Premium !

Market risk premium also known as patience premium, the return for risk is a premium for patience.

Investment in stock must often wait longer to earn a return that is higher than that provided by bond, like as much as about 20 years longer, and the riskier the investment the longer the wait is likely to be. The return for risk really is a premium for patience. Research shows that the return from common stocks was highly variable and uncertain over single-year intervals. The highest return and garnered from the market in any one year was positive 52.3% and the lowest was a negative 26.3% But once the time horizon for investing was stretched out to even just 5 years, a remarkable central tendency began to appear. The cumulative return began to converge in accordance with a statistical phenomenon known as a regression toward the mean. Over the long run, annual market swings tend to cancel each other out, making common stock investing prudent for even the cautious investor.

Definition of Rates of Return.

The investment return normally expressed in percentage is a measure of the growth of initial invested capital over certain period of time. For instance, the stock price purchase at time t, represented as Pt and the stock price increase/decrease to Pt+1 after one year, the investment return Rt is calculated as R t = [ P t+1 - Pt]/ Pt. If the dividends are paid, the calculation will adjusted to Rt=[ P t+1 - Pt+Dt]/ Pt.

Investment	arith.mean	geom. mean	Standard deviation	High Return	Low Return
S&P total return	12	10	22	43	-30
U.S. Small Stock TR	17	12	36	74	-37
U.S. LT Govt TR	5	5	8	15	-8
U.S. LT Corp. TR	6	6	7	14	0
U.S. 30 day T-Bills	4	4	1	1	0

Arithmetic rates of return and  Geometric rates of return are two difference methods of measuring average return and they rarely yield the same result from each other. For Eexample: r1 = -50% and r2 = +100%.  The geometric average is calculated as: [(1+r1)(1+r2)]1/2-1=0% but the arithmetic average is calculated as (100-50)/2 = 25%, From the result above, the geometric average is more closer to the actual investment result which you did not make any money over the two periods but arithmetic average shown 25% return. However, in many statistical models, the arithmetic rate of return is employed.

Standard Deviation as a Measure of Risk . Stock returns may be riskier or more volatile, standard deviation from statistics is a summary measure about the average spread of observations. If the S&P return are normally distributed and the standard deviation of one year return is 15%, then 2/3 of the S&P index investors annual return should fall between the range (12+15)= 27 and (12-15)= -3.