expected return

Examples of expected return in the following topics:

• Calculating Expected Portfolio Returns

  • A portfolio's expected return is the sum of the weighted average of each asset's expected return.
  • The return of our fruit portfolio could be modeled as a sum of the weighted average of each fruit's expected return.
  • W is weight and E(RX) is the expected return of X.
  • A math-heavy formula for calculating the expected return on a portfolio, Q, of n assets would be:
  • If you were playing roulette at a casino, you may not know if red or black (or green) is coming on the next spin, but you could reasonably expect that if you bet on black 4000 times in a row, you're likely to get paid on about 1900 of those spins.

• The SML Approach

  • The SML is the graphical representation of CAPM used to determine if an asset is priced to offer a reasonable expected return for the risk.
  • The market is expected to return 12% next year.
  • Expected return = 5% + 1.9*(12% - 5%) Expected return = 18.3% We expect the asset to return 18.3% and be plotted on the SML.
  • It graphs the relationship between beta (β) and expected return, i.e. it shows expected return as a function of β.
  • The Security Market Line for the Dow Jones Industrial Average over a 3 year period, with the x-axis representing beta and the y-axis representing expected return.

• Implications for Expected Returns

  • The expected return of a diversified portfolio is the expected return of each of its underlying investments times the weight the investment receives.
  • Let's make this very simple and say that bonds return 4% in a bad year, 6% in an average year, and 8% in a good year, and stocks return -5% in a bad year, 10% in an average year, and 15% in a good year.
  • Remember, things go in cycles, so we expect that if stocks do well relatively to bonds that sometime in the future, bonds will do well relative to stocks.
  • Assuming rebalancing, the expected return of a diversified portfolio is simply the expected return of each of its underlying investments times the allocation weight the investment receives.
  • Different returns are expected for different asset allocations given historical averages

• Impact of the SML on the Cost of Capital

  • There is a tradeoff between a security's price and its expected return.
  • If the price of the instrument goes up, its expected returns go down, and vice versa.
  • An instrument plotted below the SML would have a low expected return and a high price.
  • An instrument plotted above the line has a high expected return and a low price.
  • An instrument plotted on the SML can be thought of to be fairly priced for the amount of expected return.

• The Capital Asset Pricing Model

  • The market is expected to return 12% next year.
  • Expected return = 5% + 1.9*(12% - 5%).
  • Expected return = 18.3%.
  • The expected rate of return = the rate of return for a risk-free asset + beta* (the rate of return of the market - the risk-free rate).
  • Calculate a company's expected rate of return using the Capital Asset Pricing Model (CAPM)

• Expected Return

  • In finance, evaluating your expected return is important, but never as simple as evaluating a game of dice.
  • Based on your research, you realize that the stock has an expected return that is calculated thus:
  • E[R]= (ProbabilityHG)x(ReturnHG)+(ProbabilityTC)x(ReturnTC)+(ProbabilityWB)x(ReturnWB) = (0.25)(25%) + (0.60)(10%)+(0.15)(-20%) = 6.25% + 6% + -3% = 9.25%
  • If you were to invest the stock in the ski mountain, year after year, and your research proves accurate, you could expect to receive an average of 9.25% return each year.
  • That is your expected return.

• Variance

  • Variance is a statistical concept describing the range around expected return within which an investment return can be reasonably expected to fall.
  • The small number comes from the TC scenario where the stock returns 10%, which is very close to our expectation of 9.25%.
  • It means that, even though we can expect an average of 9.25% return on our stock over the course of 50 years, if we take any given year out and look at its performance, it is likely be somewhere within 13.81% above or below that figure.
  • In the discussion of expected return, we concluded that, based on your research, you can expect the Ski/Snowboard Resort in Colorado to have an expected return of 9.25% based on three distinct weather outcomes.
  • Calculating variance is a 3 step process once expected return has been calculated.

• Measuring Risk

  • The higher the risk undertaken, the more ample the expected return and the lower the risk, the more modest the expected return.
  • The firm must compare the expected return from a given investment with the risk associated with it.
  • This risk and return tradeoff is also known as the risk-return spectrum.
  • Risk aversion is the reluctance to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff.
  • For example, a risk-averse investor might choose to put his or her money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value.

• Risk and Return Considerations

  • The higher the risk undertaken, the more ample the expected return - and conversely, the lower the risk, the more modest the expected return.
  • The firm must compare the expected return from a given investment with the risk associated with it.
  • This risk and return tradeoff is also known as the risk-return spectrum.
  • Risk aversion is the reluctance to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff.
  • For example, a risk-averse investor might choose to put his or her money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value.

• Differences Between Required Return and the Cost of Capital

  • Required return and cost of capital differ in their perspectives (investor versus company) and scope (individual versus all securities).
  • Required return refers to an investor's point of view, while cost of capital refers to the point of view of a company.
  • When we speak of cost of capital, we are referring to the expected returns on all of the various securities issued by a company, often expressed as a weighted average.
  • However, since required return is from the investor's point of view, it refers to the rate of return necessary to compensate investors for taking on the risk of the individual investment.
  • The capital asset pricing model is a good representation of how to obtain required return.