Lesson 2: Risk & Return

the degree of return over and above the rate of inflation

real rate of return

rate of return used to adjust for inflation

real rate of return 1+R / 1+i - 1 x 100

rate of return an investor must earn on an investment to be fully compensated for its risk

required rate of return

a reward for investing

return

additional return needed due to relative risk of the investment compared to other, safer investment choices

risk Premium

a measure of risk or total return variability and includes systematic and unsystematic influences on asset returns measures average distance of annual returns from the average(mean) return

standard Deviation

Does beta measure systematic or unsystematic risk?

systematic

primary sources of risk

systematic or :market Driven Risk & Unsystematic or Unique (specific to secuirty)

ho do we quantify investment return

this is not a straight fwd answer. there are MANY ways to calculate 1. Holding period return 2. Arithmetic Mean Return 3. Geometric mean return 4. Internal Rate of return (Dollar-weighted Return) 5. Annualized Return 6. After tax return 7. Real Return

Seth bought ABC stock for $21 per share 6 months ago. Seth sold ABC today for $29.40 per share. What is his annualized return?

96%

annualized Return Eqn

= (1+Rp)^N - 1 Rp = return for the period being measured (month, quarterm days, etc.) N = number of periods on a year(12, 4 , 365,e tc)

Assume Jack earned a quarterly return of 3%. The annualized rate of return would be:

(1+1.03)^4 - 1 = .1255 or 12.55%

Parker buys a stock for $60 and receives dividends of $10. He then sells the stock for $100. What is his holding period return? Was this a good return?

(100-60)+10 / 60 = 83.3% good return but we don't know the holding period

A company has a required rate of return of 5%, should they make a $10 million investment that is expected to bring in $1 million of profit each year for 15 years?

-$10M CFj $1M CFj 15 Nj IRR = 5.56% yes they should move fwd with project

Melissa buys a stock for $50. She receives $4 in dividends during her holding period and sells the stock for $45. What is her holding period return (HPR)?

-2% 45-50 + 4 / 50

Three years ago, an investor contributed $15,000 to an investment portfolio. A year later, when it was worth $15,000, the investor contributed another $10,000. Another year later, the portfolio was worth $15,000 and the investor withdrew $5,000. Today, the portfolio is worth $15,000. What was this investor's dollar-weighted return over the past 3 years?

-9.07%

market has a beta of

1

What is the real return on an investment earning a 4% nominal return if inflation is 2%?

1.04 / 1.02 - 1 * 100 = 1.96%

yr1: 45% yr2: -10% yr3:-25% yr4: 30% what's the GMR

1.45x.9x.75x1.3 = 1.27 1.27 ^ 1/4 = 1.06 1.06 - 1 x 100 = 6.21%

Stan invested in the Great Growth mutual fund five years ago. His returns were 60%, -20%, 10%, 0%, and 25%, respectively. What was the geometric average return over the five years?

1.6*.8*1.1*1*1.25 ^ .2 - 1 *100 = 11.97

An ETF returned 10%, -5%, -8%, and 12% over the past 4 years. What was its geometric average return during this period?

1.87%

A CD offers 3% per quarter. What is its annualized return?

12.55%

what is the dollar-weighted return of an investment portfolio with the following cash flows over the past 3 years? beg yr 1: 50k down end of yr 1: 5k down end of yr 2: 25k out end of yr 3: 50k out

12.84%

Onica's retirement fund is expected to earn a nominal rate of 8% and the inflation rate is estimated at 4%. What is Onica's real rate of return?

3.85%

how to calculate standard deviation by hand with an example investment that returned 5%, 9%, 1%, -2%, and 7% over the past 5 years.

5 (Sum+ button) 9(Sum+ button) 1 (Sum+ button) -2(Sum+ button) 7 (Sum+ button) SHIFT 8 = 4.47%

What is real rate of return on an investment that returns a 12% nominal rate during a year in which inflation was 6%?

5.66%

a stock with beta of 1.5 should be ____ more volatile than market returns

50%

normal distributions referring to standard deviation

68% of returns will fall within +/- 1 standard deviation 95 % of returns will fall within +/- 2 standard deviations 99% of returns will fall within +/- 3 standard deviations

What is the holding period return (HPR) of an investment that cost $100, paid $25 over its term, and was sold for $150?

75%

assumes cashflow (interest/dividends) are reinvested at the same rate for a holding period of 1 year

Annualized Return

the percentage change in the investment's value from the beginning to the end of the period.

Appreciation new-old / old

a simple average return and uses the same formula you've likely seen since you were in elementary school

Arithmetic Mean Return should never be used when finding rates of returns

an indication of a securities volatility relative to the market

Beta

systematic ris is measured by

Beta

examples of unsystematic risk

Business - risk specific to a business (ops, mgmt, earnings) Country - uncertainty due to international politics financial - capital structure of the firm govt/regulation - risk of tariffs credit crisk, default risk, event risk, liquidity risk

Which of the following is a systematic risk? Country risk Exchange rate risk Financial risk Business risk

Exchange rate risk

calculates the average return over time, assuming all earnings remain invested. Calculates the compound annual return, not the simple average

Geometric Mean Return (GMR) aka TWRR or Time weighted Rate of Return

Holding Period Return eqn

HPR = (Selling Price - Purchase Price)+/- Cash Flow / Purcahse Price

a measure of return that includes capital appreciation or loss and current income

Holding Period Return *Most significant when Holding period is one year

At the beginning of Year 1, an investor buys one share of Good Chips stock for $12. At the end of Year 1, the investor receives a dividend of $1 and buys another share of Good Chip stock for $16. At the end of Year 2, the investor sells both shares for $20 each. Dollar Weighted Rate of Return (IRR)? Time Weighted Rate of Return (GMR)?

IRR = 30.48 (-12 CFj, -15 CFj, 40CFj, IRR = 30.48%) GMR for one share = -12 CFj, 1 CFj, 20CFj, IRR = 33.33%

Christine purchased 100 shares of Fly Cheap Airlines stock for $12 per share. One year later, the stock paid a dividend of $1 per share but its price dropped to $11 per share. Christine buys 100 additional shares for $11 per share. At the end of the second year, Christine sells all 200 shares for $20 per share. find IRR & GMR

IRR = 45.6% (-1200CFj, -1000CFj, 4000CFj, IRR) GMR = 33.33% -1200CFj, 100CFj, 2000CFj, IRR)

the earnings rate for a series of cash in/outflows over a preiod of time while assuming all earnings are re-invested. - equates discounted future cash flows to the present value of an asset.

Internal Rate of Return IRR Calculator does this for you CFj Key

measures how frequently returns cluster around the mean or if extreme returns occur more frequently

Kurtosis

Security A has the following returns over four years: 8%, -5%, 1%, and -1%. What are the mean return and the standard deviation for Security A?

Mean of 0.75% and standard deviation of 5.44%

examples of systematic risks

Purchasing Power Risk Reinvestment Rate Risk Interest Rate Risk Market Risk Exchange Rate Risk

involves the uncertainty of future outcomes or the possibility of an adverse result

Risk

risks that are inherent in the "system". these are non-diversifiable, regardless of how many securities and industries are combined in a portfolio.

Systematic risks

risk that can be diversified away by combining multiple asset classes and industries in a portfolio

Unsystematic risk

the amount of cash the investment pays back to the investor on a regular basis - expressed as a percentage of the amount invested.

Yield

arithmetic mean

calculated by totaling all the results and dividing by the number of results

A risk due to uncertainty surrounding the outcome of an election is known as a business risk. country risk. financial risk. interest rate risk.

country risk.

the investor's expectations of inflation

expected inflation premium

the return an investor believes an investment will earn in the future.

expected return

data is peaked at the mean and has more observations in the tail

high Kurtosis aka leptokurtic date

expected returns depend on many internal and external forces

internal: Historical return, expected risk, type of investment vehicle, quality of management, how the investment is financed, size of customer base external: Fed reserve actions, shortages, war, price control, political events

dollar weighted returns tend to be less thatn average market returns bc many investors buy stocks after they rise in value and sell stocks after they fall in value

investor return gap

data has a relatively short short peak at the mean as well as thinner tails

low kurtosis aka platykurtic data

Security B has the following returns over four years: 4%, 5%, -1%, and -6%. What are the mean return and the standard deviation for Security B?

mean: .5 Std dev 5.07

data that fits a bell shaped curve is said to be

normally distirbuted

geometric mean return

nth root of ((1+r1)(1+r2...(1+rn)) - 1 x 100 (nth root is also "to the power of 1/n)

Yield + Appreciation = ?

total return

example of positive skew for bonds

treasury bills since negative return is not possible

true or false: the arithemtic mean will alsways be greater than or equal to the geometric mean

true