Lecture 4, Chapter 5: Risk and Return in Financial Markets

Describe geometric and arithmetic average and the difference between them

Arithmetic average is the the sum of the return divided by the number of returns. Geometric average takes into account the compounding that occurs from period to period. Therefore, geometric average is better when measuring returns. This is the one we want to use when calculating average returns!

What is covariance?

Covariance is a measure of how much two random variables vary together. The mean value of the product of the deviations of two variates from their respective means.

What is expected return and how is it calculated?

Expected return is the profit or loss an investor anticipates on an investment that has known or expected rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then summing these results. For example, if an investment has a 50% chance of gaining 20% and a 50% change of losing 10%, the expected return is (50% * 20% + 50% * -10%), or 5%.

What is excess return?

Is the difference in any particular period between the actual rate of return on a risky asset, and the actual risk-free rate. Excess return is the reward for taking risk. Is what I get above the risk-free rate, and the return I get for taking risk. Excess return = Expected return - risk-free rate

What is a real rate of return and how is it calculated?

Is the nominal rate of return adjusted for inflation. This is the growth rate of my purchasing power. This method expresses the nominal rate of return in real terms, which keeps the purchasing power of a given level of capital constant over time. The Formula for the Real Rate of Return Is Real rate of return = Nominal interest rate - Inflation rate

What is a nominal rate of return and how is it calculated?

Is the rate of return earned on an investment without any adjustment for inflation. This is the growth rate of my money. The formula is: Current market value−Original investment value / original investment value ​

What is correlation?

Is the relationship between two variables. You can put two stocks in a portfolio as a way to diversify your risk, and see how the stocks move together and how they correlate to each other. If the one goes down, hopefully the other goes up and compensates for the other. Correlation is the measure of this, and negative or low correlation is the best. Correlation coefficient: 𝜌_𝐷𝐸∈[−1:1] 1 would mean stocks and bonds always go up and down together −1 would mean stocks and bonds always move in opposite directions =0 would mean there is no pattern

What is the holding period return (HPR) and how is it calculated?

It describes how much you earned over the time period of your investment. HPR = (PT - P0 + income from distributions) / P0 (T= usually end of time period) (0 = beginning) HPR = (ending price of a share - beginning price + cash dividend) / beginning price

What is the Sharpe ratio?

The Sharpe ratio is used to help investors understand the return of an investment compared to its risk. Subtracting the risk-free rate from the return allows an investor to better isolate the profits associated with risk-taking activities. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return. Sharpe ratio = E(r) - rf / StdDev(r)

What says the basic law of finance about risk and return?

The basic law of finance is that higher risk should be compensated with higher return.

What is standard deviation?

The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean. Is the average deviation from the average. How much does the returns deviate from the average. This, is a measure of risk and the standard measure in the market. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation. When applied to the annual rate of return of an investment, the standard deviation sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, which shows a larger price range. For example, a volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low.