week 2: typology Flashcards
What did Robert Shiller say about prices?
“Prices are actually very volatile so not an efficient forecast”
In an efficient market what forecasts profit?
PRICES
e.g. an increase in prices correlates to stronger demand or weaker supply
how is equity derived from this?
cash + fixed assets - loans
what it owns - what it owes!
Suppose a firm has 500 shares outstanding. The book value of each share is what?
Book value of each share is:
⭐ Ratio of Equity to the total number of shares outstanding ⭐
⭐ EQUITY/NO. OF SHARES OUTSTANDING ⭐
E.g. here 3000/500 = 6
Suppose by the end of the year, the firm made 1000 in profits, if management of firm distributes profits as dividends (2 per share) the balance sheet will be …?
The same as that on Jan 1, 2017
However if firm makes 1000 in profits + firm DOES NOT distribute profit as dividends, what happens to the balance sheet?
Cash increases to 2000, so equity is now 4000
What is the new book value of shares now?
4000/500 = 8
What are dividends?
Dividends are payments made by a corporation to its shareholders as a distribution of profits.
They are typically distributed regularly, usually quarterly, and are a portion of the company’s earnings.
How will the equilibrium price (market value) of shares be determined on Jan 1, 2017 in the competitive stock exchange market?
depends on expectations of investors
Case 1: Investors do not anticipate any profits for 2017 & any year after
What happens to book value of share?
stays at 6
Case 2: investors anticipate increase in profit by 1000 but no additional future profits & company doesn’t offer dividends
Market price of each share is now 8
Case 3: investors anticipate increase in profit by 1000 but no additional future profits PLUS company offers dividends
Market price of each share is now **8 + dividend **
What is the famous Modigliani - Miller theorom?
Shows that in markets without friction, the value of the firm is the firm’s capital structure + dividend policy.
Note: when investors fully anticipate the profits generated in 2017, competition ensures that the market price immediately adjusts on Jan 1st.
The above cases are a simple demonstration of the __________ Hypothesis?
Efficient Market Hypothesis - prices provide a forecast for profits
What is the random walk model?
“The best predictor of tomorrow’s price is today’s price”
What is the formula for the random walk model?
P(t+1) = P(t) + ε(t)
ε(t): errors that are independently distributed across time + drawn from a normal distribution with mean 0
Explain the random walk model in detail
Randomness: Imagine taking a walk where each step you take is random. You might take a step forward, then two steps back, then sideways, and so on. In the same way, the random walk model suggests that the movement of prices or values in financial markets is unpredictable and can go in any direction without following a specific pattern.
Independence: In a random walk, each step you take is independent of the previous step. For example, the direction you go in the next step is not influenced by the direction you went in the previous step. Similarly, in the financial context, future price movements are considered independent of past movements. This means that just because a stock went up yesterday, it doesn’t mean it will go up again today.
Efficiency: The random walk model assumes that financial markets are efficient, meaning that all available information is already reflected in current prices. This implies that there are no “undervalued” or “overvalued” assets because all relevant information is already priced into the market. Therefore, future price movements cannot be predicted based on past information or patterns
In essence, the random walk model suggests that the best forecast for the future price of an asset is its current price, as future movements are unpredictable and random. This concept has important implications for financial markets and investment strategies
What is a random walk with growth?
It’s where asset returns are normally distributed w mean μ (drift) and variance σ^2 (volatility)
asset returns follow a random walk pattern with a consistent trend or growth component. The returns are normally distributed around the mean with a certain level of variance or volatility, representing the randomness and uncertainty in the movement of asset prices over time.
What are asset returns?
Asset returns refer to the change in value of an investment or asset over a specific period of time, typically expressed as a percentage. It represents the gain or loss experienced by an investor from holding an asset during that period.
For example, if you purchase a stock for $100 and it increases in value to $110 over one year, the asset return would be 10%
As random processes are displayed on a normal bell curve with thin tail distribution, what does this say about results?
Unlikely to see extremes as most results will be covered within 2 standard deviations
What would we call μ in the model?
Drift, this would be 0
What would we call variance σ^2 in the model?
Volatility, this would be 1
What are ‘fat tails’ or excess volatility?
In summary, “fat tails” or excess volatility refer to the observation of more extreme movements in financial markets compared to what would be expected based on theoretical models like the normal distribution
suppose, we plot the monthly movements of the Dow Jones index on a chart according to their frequency
- Theoretical models predict the plot would follow the Bell Curve
- The actual plot would show much less clustering around the average & many more extreme movements.
If the movements followed the normal distribution
An annual decline of greater than 10% would happen once ** every 500 years**
In the Dow Jones, an annual decline of greater than 10% it has happened once every _____ years
5 years
If the movements followed the normal distribution, Declines of 20%+ would be extremely unlikely but in fact there were _ such crashes during the past century.
9
These observations of fat tails contradict the predictions of the …
efficient market model
Wat does this mean
What is the fundamental principle of optimal forecasting?
The forecast must be less variable than the variable forecasted.
forecast in this case: p(t)
variable forecasted: p(t+1)