Risk and Return in Investments

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Questions and Answers

What is the holding period return (HPRt) formula to calculate the return from an investment over a specific period?

$HPRt = \frac{PT + Pt}{2}$

$HPRt = \frac{PT \times Pt}{100}$

$HPRt = \frac{PT - Pt}{Pt}$ (correct)

$HPRt = \frac{Pt - PT}{PT}$

Which zero-coupon bond has the highest holding period return (HPRt)?

Bond C (correct)

Bond A

Bond B

They all have the same holding period return

What is a key reason why the holding period return (HPRt) cannot be directly compared among different bonds?

They have different coupon rates.

They require different initial investments.

They have different liquidity levels.

Their holding periods differ. (correct)

Which factor is NOT mentioned as impacting the interest rate?

Market risk Signup and view all the answers

If an investor wants to compare the returns of multiple bonds with different holding periods, what should they calculate?

One-year-equivalent-returns Signup and view all the answers

What is represented by $Pt$ in the HPRt formula?

The current market price of the bond Signup and view all the answers

What is the par value of the zero-coupon bonds mentioned?

$100 Signup and view all the answers

Which bond has the longest time to maturity?

Bond C Signup and view all the answers

What does the effective annual rate (EAR) take into account that the annual percentage rate (APR) does not?

Re-investments of returns Signup and view all the answers

For a bond bought at €80 with a payout of €100 after 5 years, what is the holding period return (HPR)?

0.25 Signup and view all the answers

According to the relationship between interest rates and inflation, which statement is true regarding the real interest rate and nominal interest rate?

Real rates are adjusted for inflation Signup and view all the answers

What happens to the effective annual rate (EAR) as the time to maturity increases?

It is less than the APR Signup and view all the answers

What formula represents the relationship between nominal interest rate, real interest rate, and expected inflation rate?

rnominal = rreal + πexpected Signup and view all the answers

After reinvesting the returns from buying a bond for €80 and getting €100 back, how much would you have if you reinvested it immediately?

€125 Signup and view all the answers

What does the annual percentage rate (APR) represent in financial terms?

The simple interest earned per year without considering compounding Signup and view all the answers

In the formula for holding period return (HPR), what does P0 represent?

The purchase price of the investment Signup and view all the answers

What is one advantage of using logarithmic returns?

They allow for easy aggregation of high frequency returns. Signup and view all the answers

When estimating future investments, what approach can be used?

Define scenarios and assign probabilities to each scenario. Signup and view all the answers

What does the Sharpe ratio measure?

The additional return gained per unit of risk taken. Signup and view all the answers

How can historical returns inform the probability distribution of future returns?

They provide a basis for assuming a normal distribution. Signup and view all the answers

In regards to exchange rates, what does the symmetry of logarithmic returns refer to?

The return differs in magnitude, but not in sign for quotations. Signup and view all the answers

What is a common misconception about the variation of historical returns?

Historical returns are always identical across different periods. Signup and view all the answers

What might lead lenders to increase compensation during inflation?

Projected increases in the cost of money over time. Signup and view all the answers

What is typically necessary to describe a normal distribution of returns?

Both the mean and the standard deviation. Signup and view all the answers

Study Notes

Risk and Return from Historical Record

Portfolio theory categorizes investments primarily by risk and return.
Return: the gain or loss on an investment relative to the initial investment.
Interest rate factors include:
- Supply of capital by households
- Demand for capital by businesses
- Government's net supply/demand (e.g., actions by the central bank).

Comparing Zero-Coupon Bonds

Comparing zero-coupon bonds with different maturities and a par value of 100 involves evaluating holding period return (HPR).
HPR is the return over a specific time period, like from time 0 to time T.
It's analogous to an interest rate, but the interest rate is fixed upfront, whereas HPR varies over the holding period.
HPR is calculated as (Price at the end of the period / Initial Price) - 1.

Holding Period Returns

Holding period returns increase as bond maturity increases.
Comparing bonds with different holding periods isn't straightforward.
One must standardize returns (e.g., convert to "one-year-equivalent returns") to make a fair comparison.

Annual Percentage Rate (APR) vs. Effective Annual Rate (EAR)

APR: A simple way to calculate annual percentage rate. APR does not consider reinvestment.
EAR: Considers reinvestment, thus offering a more accurate measure of returns, given that the money earned over a period of time is reinvestment in the same or similar instrument. A more accurate result than APR, which does not.
- The difference between APR and EAR is larger with longer maturities.

Relationship between Interest Rates and Inflation

The Fisher equation describes the relationship: Nominal interest rate = Real interest rate + Expected inflation rate.
The nominal rate reflects compensation for lending + the price increases expected for the currency used. Real interest rate does not factor in inflation.
Investors prioritize real interest rates over nominal as they relate to purchasing power and real value.

Mean Scenario Returns

Historical returns can be used to assess investment estimations, although they don't consider future scenarios.
Assigning probabilities to future scenarios can help estimate expected returns for investments where future outcomes are uncertain.

Percentage vs Logarithmic Returns

Logarithmic returns are easier to aggregate temporally compared to percentage returns.
Logarithmic returns also show more symmetry (positive and negative changes are treated equally from a log perspective).

Sharpe Ratio

The Sharpe Ratio is calculated by dividing risk premium by standard deviation.
It measures reward relative to variability.
A higher Sharpe Ratio indicates greater return for a given amount of risk.

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Description

Explore the concepts of risk and return in investment portfolios. This quiz covers the evaluation of zero-coupon bonds and the calculation of holding period returns over various maturities. Test your understanding of key financial metrics and theories related to investment strategies.