Measuring Investment Returns: Simple Case
- Invest W0 at the beginning of the period
- This investment is worth W1 at the end of the period
Complications
What if there are cash flows during the investment period?
Dollar Weighted Returns
It is analogous to internal rate of return
Time Weighted Returns: procedure
1) Divide whole investment period into sub-periods based on when additions and withdrawals occurred
2) Determine returns for each sub-period (thus, you need the portfolio's value at the end of each sub-period)
3) Compound the returns
4) Annualize the comp
Time Weighted Returns
Averaged returns that assume that no cash was contributed or withdrawn during the averaging period, meaning after the initial investment
Equity Valuation Basis Models
- Dividend Discount Models
- Price/Earning Ratios and Multiple Approach
Intrinsic Value (IV)
- Self assigned Value
- Variety of models are used for estimation
Market Price (MP)
Consensus value of all potential traders
Trading Signal
- IV > MP ? Buy
- IV < MP ? Sell or Short Sell
- IV = MP ? Hold or Fairly Priced
Dividend Discount Models: General Case
The basic idea is that the value of any asset is simply the discounted value of all the cash flows (to be received) associated with the asset
Dividend Discount Models: Zero Growth
dividends are assumed to remain the same forever. Hence, the cash flows paid by the security constitute a perpetuity
The Constant Growth Model
The constant growth model assumes that dividends grow at a constant rate, denoted g, forever
The growth rate g
ROE xb
ROE
Return on Equity for the reinvestment of the firm's earnings
b
plowback or retention percentage rate (= 1 ? dividend payout ratio)
The Multiple-Stage Growth Model
The multiple-stage growth model assumes that before T the dividend growth rates can be changing from year to year in the way you find more appropriate. Then, dividends grow at a constant rate g from T onward
How do you use a dividend discount model if the firm has either never paid dividends or has recently suspended the payment of dividends?
You need to estimate:
-when dividends will start to be paid
-how much they will be
-how they will grow over time
Price Earnings Ratios
Current share / earnings per share
P/E Ratios are a function of two factors
-Required Rates of Return (k)
-Expected growth in Dividends (g)
Multiple ratio approach or relative valuation approach
Relative valuation approaches estimate the value of common shares by comparing market prices of similar companies, relative to variable such as:
- Earnings
- EBITDA
- Cash flow
- Book value
- Sales
To estimate the intrinsic value of a stock using the P/E approach:
1 Choose a group of comparable firms
2 Calculate the average P/E ratio for the group
3 Estimate earnings per share for the company for next 12 months
Problems with P/E
Earnings are a creation of the matching principle and are subject to re-statement and manipulation:
There is no clear indication of what a high P/E actually means
Similarly companies with low P/Es might be interpreted as having few growth opportunities OR
Market Indexes
Price-weighted Average
Value-weighted Average
Equally Weighted Index
Price Weighted Index
involves two steps:
1) First, sum the prices of the stocks included in the index
2) Second, divide this sum by the "divisor
Why is this method called price weighting?
Each stock return is weighted by the respective stock price
Why do we need a "divisor"?
In order to ensure the continuity of the index when corporate events occur
Value Weighted Index
1 First, multiply the price of each stock in the index by the number of shares outstanding to obtain the market value of that stock at time 0
2 Second, sum the market values of the stocks in the index at time 0 to obtain the total aggregate market value o
Why is this method called value weighting?
Stock returns are weighted by the stock's market value in the total aggregate market value of the stocks in the index
Equally Weighted Index
1 First, for each stock in the index, compute the gross return by dividing a
stock's price at time t to its price at time 0
2 Second, compute the average gross return (ARt) from dividing the sum of all
the gross returns in the index by the number of stock
Why is this method called equal weighting?
Stock returns are equally weighted in the total aggregate investment value (of the stocks in the index)
Unlike price- or value-weighted indices, equally weighted indices do not correspond to a buy-and-hold portfolio strategy