A. Securities Markets

1. Commission: Fee paid to broker for making the transaction
• SG: 0.5%
• HK: 1%
• CHN: 0.05%
• US: $9.9/trade (Irespective of the amount of the trade) 2. Spread: Costof trading with dealer • Bid: Price the dealer is willing to pay • Ask: Price the dealer will sell •$\text{Spread} = \text{Bid} - \text{Ask}$Depth of the market: Total number of shares offered for trading at the best bid and ask prices. • Market orders are highly volatile and can be executed at any price. A.2. Margin Trading Borrow money, Buy stock. Each broker would have a minimum cost to open a margin account. This minimum amount is called the initial margin requirements. There are two margin requirements: 1. Initial margin requirement (IMR): Amount that needs to be payed as a down payment. 2. Maintenance margin requirement (MMR): Equity percentage that needs to be maintained in a margin account. Buying on margin = Leveraging your position The margin is the asset placed as a collateral as a percentage of stock position. • Buying on margin is exteremely risky and magnifies both the profits and loss. Sitaution: Margin call The current value of equity equals or is less than the maintenance margin requirement. • Ignore interest if considering a decrease in equity immediately after a purchase • Include interest if considering a decrease in equity over a time period such as one year Important Relationships / Concepts: •$\text{Equity} (E)$= Amount of own money invested •$\text{Market value of stock position} \text{ (MVSP)}$= # of shares x current price •$\text{Borrowed amount} \text{ (B)}$= Amount of money borrowed from the broker •$\text{interest} \text{ (I)}$= Interest paid on borrowed money •$\text{additional cash} \text{ (C)}$= Additional cash paid to the broker on margin calls (If any) •$\text{dividend} \text{ (D)}\$ = Dividend from stocks

$$E = \text{MVSP} - L - I + C + D$$ $$\frac{E}{\text{MVSP}} \le \text{MMR}$$

A margin call occurs,

$$\text{MVSP} \le \frac{\text{L}-\text{I}+\text{C}+\text{D}}{1-\text{MMR}}$$

A few key things to remember:

1. How to calculate margins at different stock prices

2. Calculating the rate of return for investments on margin

$$\text{RR}= \frac{\text{MVSP} - \text{B} - \text{I}}{\text{E}}-1$$

2.1 With Interest

2.2 Without Interest

Rate of Return on Investment by margin trading

$$\text{RR} = \frac{\text{Final market value}-\text{Loan} - \text{Interest} + \text{Dividend}}{\text{Initial investment}} - 1$$

A.3. Short Sales

What is shorting?

• Borrow shares of a stock and sell thm on market at current price in hope that the price will decrease.
Federal Reserve Board requires all short sale accounts to have 150% of the value of the short sale at the time the sale is initiated.

The mechanics

1. Borrow stock from a broker/dealer, must post margin
2. Broker sells stock. Deposits proceeds and margin into a margin account
• You are not allowed to withdraw the proceeds until you ‘cover.’
3. Covering or closing out the position:
• Return the stock title back to the party from which it was borrowed

All the formulations remain almost the same as trading on margin, except the equity.

$$\text{Equity}=\text{Initial margin account}-\text{MVSP}-\text{Dividends}$$

Market value of stock position and dividends are subtracted as the stocks are borrowed.

• The lender lends the stock with additional interest and commission imposed on the lending.`

$$\text{Initial margin account} = \text{Proceeds from sale}+\text{Cash deposited to meet margin requirements}$$

Furthermore, margin cll occurs when, $$\text{MVSP} \ge \frac{\text{Margin Account} - \text{Dividend}}{1+\text{MMR}}$$

Rate of Return on Investment by shorting on margin

$$\text{RR} = \frac{\text{Proceeds from sale}-\text{Repurchase cost - Dividend}}{\text{Initial investment}}$$

B. Risk and Return: Past and Prologue

B.1. Rates of Return

1. Holding period returns

$$HPR_t = \frac{(P_t - P_{t-1} + D_t)}{P_{t-1}}$$

1. Arithmetic rates of return vs. Geometric rates of return

$$HPR_{AAR} = \frac{1}{T}\sum^T_{t=1}HPR_t$$

$$HPR_{GAR} = \frac{1}{T}\prod^T_{t=1}[1+HPR_t]^{1/T}-1$$

The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period.

Conclusion: Geometric mean is more accurate in real world calculation

C. Class notes

Singapore is one to the top most expensive city to live in the world.

What can we learn from buffett’s investment strategy?

• Value investing: Fundamental analysis