Chapter 5: Risk. Return, and Historical Record Flashcards
What is Portfolio management? What is the fundamental aspect and goal of Portfolio management?
Portfolio Management: determining the mix of assets to hold in portfolio
* stocks
* bonds
* cash
* real estate
* alternative invetsments
Fundamental Aspect: choosing assets which are consistent with invetsor’s risk-tolerance and return objectives
Goal: to achieve optimum return for the given level of risk
Risk Return Relationship: what is the ?
Higher risk → “?” return
Lower risk → “?” return
Higher risk → higher return
Lower risk → lower return
What do we mean by “Expected” or “Required” return?
Expected Return: Hint.. think of formula! How do we calculate this?
By taking the average return the investor anticipates based on past performance or projections
Formula: (Prob. of outcome x return of outcome)
- what we’re expected to make
Required Return: is the minimum return an investor needs to earn to justify taking on the risk of the investment
- Considers risk free rate, risk premium, and inflation
- If I take on this risky asset, this is what I require
Should you take on an investment whose expected return is below the expected return, should you take on this investment?
No, the required return is the minimum rate you would want for taking on a risky asset.
But teh expected rate is what you want! If teh expected rate (what could be the actual rate) is less than your minimum return… don’t take it. Not attractive
What factors influence Interest rates?
Supply – saving, households
* when households save more (increased supply of money), it puts downward pressure on interest rates
Demand —businesses (to finance invetsments in plant, equipment, and inventories)
* because of this increased demand, interets rates go up
Government’s Net Supply — central bank actions
* insteases money supply by lowering interest rates, or by purchasing government bonds (so central gov gets money) - called quantitative easing
The expected rate of Inflation
* people will demand for higher interets rates to compensate for loss of purchasing power
Nominal Rate vs Real Rate
Nominal rate: is the growth rate of your money
Real rate: real rate of your purchasing power
When does the Real rate become negative?
when the inflation rate exceeds the nominal interest rate.
What is HPR (Holding period of Return)
Total return earned on an invetsmnet over the period for which it is held
* takes into account any capital gains or losses due to changes in the investment’s price during the holding period
* also any income or dividends recieved
What is Variance and Standard Deviation?
Also, what does a higher variance and lower variance (+ SD) tell you?
Variance (σ²): shows you how spread out the returns of an asset from its average return (mean)
* Higher variance means returns are more spread out
* You’d prefer low variance, as returns tend to not fluctate, but are more stable and closer towards the average return
Standard Deviation (σ): express the average amount by which the returns deviate from the mean (average return).
* If the standard deviation is high, it means the returns can swing widely; if it’s low, the returns are more consistent.
You’d prefer low using both
Ex. Suppose you have two assets:
- Asset A has a low standard deviation (e.g., 2%), meaning its returns tend to fluctuate only a little around the average.
- Asset B has a high standard deviation (e.g., 10%), meaning its returns are more volatile and can swing widely.
Define:
Excess Return
Risk Premium
Sharpe Ratio
Excess Return: Difference between actual rate of return and risk-free rate in a given period.
- Actual Rate - Risk free Rate (rf)
Risk Premium: Difference between the expected HPR on a risky asset and the risk-free rate.
- Expected return (expected HPR) — Risk-free Rate
- premium for taking on a risky asset
Sharpe Ratio: helps you compare investments by showing which one offers the best return for the risk taken. The asset with the higher Sharpe ratio is better value for per unit of risk
* A higher Sharpe ratio means that the investment is providing a better return relative to the risk. It shows you’re getting more return per unit of risk.
* A lower Sharpe ratio means that the return isn’t enough to justify the risk being taken.
The Normal Distribution, talk about it and expecially how the data points are plotted
what happens if the returns are asymetric
In a normal distribution,
* the data is perfectly symmetrical around the mean. This means that the left and right tails of the distribution are mirror images of each other.
This means:
Data points that are closely packed around the mean, results in a narrow, steep bell curve. — smaller SD
* Means most values are similar to the mean
Also,
- Data points that are more spread out from the mean. The bell curve becomes wider and flatter.
Means most values are greater than/or less than the mean
Standrad Deviation is a good measure of risk when returns are symmetric, meaning, When returns are symmetrical, the standard deviation accurately reflects both the upside potential and the downside risk because the volatility (spread of returns) is balanced.
- If the returns are asymmetric—for example, if there are more chances of extreme negative returns (downside risk) than extreme positive returns—then standard deviation doesn’t capture this imbalance effectively.
- essentially, the chart does not account for extreme negative or positive returns
What if excess returns are not normally distributed? What do we consider?
skewness and kurtosis
Define skewness and kurtosis
Skewness: Measures asymmetry in the distribution of returns.
Positive Skew (Right Skew): (hill starts left and moves to right)
* The distribution has a longer or fatter right tail. This means extreme positive returns are more common.
Negative Skew (Left Skew): (hill starts right and moves to left)
* The distribution has a longer or fatter left tail. This means extreme negative returns are more common.
Kurtosis: Measures the likelihood of extreme values and tail thickness.
- High Kurtosis: Indicates “fat tails” with more probability mass in extremes.
Define Value at Risk (VaR) and Expected Shortfall (ES)
Value at Risk (VaR): Measures potential loss at a specified percentile of the return distribution.
* You might ask, “How much would I lose in a fairly extreme outcome, for example, if my return were in the 5th or 1st percentile of the distribution?” This loss is called the value at risk
- In a extreme outcome, how much of my return would I lose?
- Ex. 1% VaR is the return below which 1% of returns fall.
Expected Shortfall (ES): looks at the average of the worst losses beyond a certain point, rather than just the worst possible loss itself.
* Provides a more detailed view of downside risk compared to VaR.
- Using a sample of historical returns, we would estimate the 1% expected shortfall by identifying the worst 1% of all observations and taking their average
Ex.
Imagine you’re an investor, and you’re concerned about the worst 5% of cases (meaning you’re looking at really bad outcomes).
- If you use Value at Risk (VaR), it tells you the loss at the 5th percentile—essentially, the worst loss that might happen 5% of the time.
- Expected Shortfall (ES) goes one step further. It tells you the average of all those really bad outcomes, not just the single worst one.
Define: Lower Partial Standard Deviation (LPSD) and Sortino Ratio (replaces sharpe ratio)
Lower partial standard deviation (LPSD): looks at the negative side of risk—the downside. It measures how much an investment’s returns fall below a certain target, typically the risk-free rate
* Computes SD only using negative excess returns.
Sortino Ratio: a way to measure an investment’s performance relative to its downside risk (LPSD).
- It shows how much extra return you get for every unit of downside risk taken.
