Securities markets and trading

A. Securities Markets

A.1. Trading Costs

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
   • $\text{Spread} = \text{Bid} - \text{Ask}$

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.

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,

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

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

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.
• Buy the stock at a lower price and return to the lender

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:
   • Buy the stock.
   • 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, $$\text{MVSP} \ge \frac{\text{Margin Account} - \text{Dividend}}{1+\text{MMR}}$$

The initial investment is the down payment of the IMR.

B. Risk and Return: Past and Prologue

B.1. Rates of Return

1. Holding period returns

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

2. Arithmetic rates of return vs. Geometric rates of return

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

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

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