Econ Notes
- 1 Geometric Series
- 2 Real Estate analogy
- 3 Real Estate numbers
- 4 Multivariate Hypergeometric Dist
- 5 Modeling COVID-19
- 6 Linear Algebra
- 7 QR Decomposition
- 8 Singular Value Decomposition
- 9 Complex Numbers
- 10 LLN and CLT
- 11 Two meanings of probability
- 12 Heavy tailed Dist
- 13 Multivariate normal dist
- 14 Univariate Time Series with matrix algebra
- 15 Linear Programming
- 16 Optimal Transport
- 17 Von Neumann Growth model
- 18 Dynamics in One dimension
- 19 AR1 Process
- 20 Finite Markov Chain
- 21 Inventory Dynamics
- 22 Linear State Space Models
- 23 The Samuelson Multiplier-Accelerator
- 24 Kesten Process and Firm Dynamics
- 25 Wealth Distribution Dynamics
- 26 Kalman Filter
- 27 Shortest Path
- 28 Cass-Koopman Planning Problem
- 29 Cass-Koopman Competitive Equilibrium
1 Geometric Series
Summary
LINEAR PROG ASSUMPTIONS INPUT Cost-function, decision-variable OUTPUT optimal-decision-variables
OPTIMAL TRANSPORT is example of LINEAR PROG Two types of nodes, supply nodes(initial object) and demand nodes(terminal object) Each initial object has required min capacity Each terminal object has required min capacity
The decision variable are basically the intensity of edge between these nodes.
More intense edges mean more items delivered between nodes.
2 Real Estate analogy
2.1 Price, Market Cap
- Assume only 1 share , even though stocks may have millions of shares
- Share Price = Market Cap
- we will call Share Price, “Price”
- Share price and Market Cap is DYNAMIC whether your neighbor gets gentrified over time
2.2 Book value = Equity
Book value is basically initial cash investment value, excluding mortgages
- ASSUMING NO LIABILITY AKA NO MORTGAGE
- Book value(Shareholder’s Equity) is the STATIC purchase price of the property
- At the time of purchase you set the Book value and synchronize the “Price” with Book value
- Book value = Share Price = Market Cap, this is only true at the time of purchase
- As property appreciates, Price appreciates but not Book value
Example:
- purchase 200k house ALL IN CASH in 2010
- Book value = Share Price = Market Cap = 200k
- After 5 years, house appreciates to 300k
- Book value = 200k
- Share Price in 2015 = Market Cap in 2015 = 300k
2.2.1 What happens if you add Liability
- purchase 200k house 30k downpayment equity, 170k mortgage
- Book value = 30k
- Share Price = Market Cap = 200k
- After 5 years, house appreciates to 300k
- Book value = 30k
- Share Price = Market Cap = 300k
BOOK VALUE IS BEST USED FOR COMPUTING CASH-ON-CASH RETURNS, NOT AS ASSET VALUE!!
2.2.2 Book value (Equity) is NOT market cap
- Tesla needs to raise funds so it issues 10 shares at 5 dollars each (thus raising $50), price of each share goes to 100 in the NASDAQ a week in due to speculation.
- Shareholder equity remains $50 on the COMPANY’S balance sheet and $50 book value.
- note: the shareholder’s individual networth/equity may have increased if he held onto the stock but that has 0 bearing on the COMPANY’s balance sheet
- Shareholder equity remains $50 on the COMPANY’S balance sheet and $50 book value.
2.3 Asset = Book Value(Equity) + Liability
- Asset = Liability + Equity
- House = Mortgage + Downpayment
Ideally compare home purchase price with Asset Value
2.4 Revenue, Sales vs Earnings, NetIncome
- Revenue = Total money made from any source
- Sales = Total money made from CORE business source
- Earnings = Revenue - Expenses
- Earnings = Net Income, colloquially
- Sales is more important to understanding core business health
- In real estate terms,
- Revenue is your rental income and money you made selling old equipment on ebay
- Sales is just your rental income
- Earnings is what is left after rental income is used to pay maintenance, handyman, tax.
2.5 Free Cash Flow(FCF) vs Cash Flow
- Free Cash Flow = Cash_Flow - (Operating_Expense + Investments)
- In real estate term
- Cash flow = Sales = Rental income
- Free Cash Flow = Earnings
- Free Cash Flow is how much actual cash you have after paying the handyman, repairs, installing new lights of your real estate
However if Landlord allows Tenant to pay later (basically like credit card debt), then Free_Cash_Flow < Earnings
2.6 PE ratio (Price to Earnings)
- Market_Cap/Earnings = Price_per_Share/Earnings_per_Share
- (Zillows price for house)/(Rental income after expenses, insurance, tax)
As a new buyer, you want a undervalued house that is cheap on Zillow with good rents which is a low PE Ratio.
A house in Paris, would be expensive with little rent income which is a high PE Ratio.
2.7 PEG Ratio (Price to Earnings Growth)
- PE_Ratio/Growth_Rate
- Assume you raise rents 5% each year
- PE_Ratio/5
Opinion: why not just use Earning Growth Rate with PE Ratio separately instead of this
3 Real Estate numbers
3.1 Compared to Real Estate rehab home
- A 300k home delivering 30k rental pre-tax
- Fixed up it is worth 500k
- Cap rate is ROI = 10%
- PEratio at 300k market cap is 300k/30k = 10
- PEratio at 500k market cap is 500k/30k = 16
3.2 Compared to Real Estate sticker price home
- Typical cap rate is 5%
- A 1M home delivers 50k rental
- PEratio at 1M = 20
3.3 10 PEratio -> Great, 20 -> mediocre, 40 -> bad
- Places in shanghai a 1M home delivers a 25k rental
- PE ratio at 1M = 40
HOWEVER YOU MUST REMEMBER GROWTH COMPANIES GROW, High PE ratio like 80 is plausible RENTAL INVESTMENTS ARE MORE LIKE BLUE CHIPS, High PE ratio is bad
- Look at PEratio of bluechips
- JPM 11
- HD-home depot 25.79
- GM-general motors 5.34
