Municipal Bonds and Stock Indexes Overview

Municipal Bonds - Advantages

Federal tax exempt: Interest earned is not subject to federal income tax. State tax exempt: If the bond is issued in the state of residence, the interest is also exempt from state taxes.

Revenue Bonds vs. General Obligation Bonds

Revenue Bonds: Interest is paid from specific revenue-generating projects (e.g., toll roads, fee-based recreation). General Obligation Bonds: Proceeds fund a variety of the municipality's needs, and interest is paid from the municipality's general funds.

Municipal Bonds - Nuveen Commercial

The commercial highlighted the tax advantages of municipal bonds, asking, "Aren't you tired of losing your bond income to taxes??? With Nuveen tax-exempt municipal bonds, keep all the income!"

Municipal Bonds - After-Tax Yield Calculation

Formula: ATY = Coupon Rate × (1 - Marginal Tax Rate). Example: For a 5% corporate coupon bond and a 30% marginal tax bracket: ATY = 0.05 × (1 - 0.30) = 0.035 or 3.5%. For a 40% tax bracket: ATY = 0.05 × (1 - 0.40) = 0.03 or 3%.

Municipal Bonds - Tax-Free Yield Impact

Everyone would buy the bond, increasing demand. Higher demand leads to higher prices and lower yields. The last buyer to benefit is the one in the highest tax bracket (e.g., 40%). Buyers in lower tax brackets stop buying once the yield reaches their after-tax equivalent (e.g., 3.5% for a 30% bracket).

Municipal Bonds - Before-Tax Yield Calculation

Formula: BTY = Muni Yield / (1 - Tax Rate). Example: Muni Yield = 3%, Tax Rate = 30%: BTY = 0.03 / (1 - 0.30) = 0.043 or 4.3%. Tax Rate = 40%: BTY = 0.03 / (1 - 0.40) = 0.05 or 5%.

Municipal Bonds - Risks

Liquidity Risk: Municipal bonds are thinly traded, making them difficult to buy or sell. Stale Pricing: Due to poor liquidity, prices may not reflect current market conditions. Rating Risk: Credit ratings (e.g., AA, AAA) may be stale or not reflect comparable risk to corporate bonds of the same rating.

Stock Indexes - Purpose

Serve as benchmarks for performance evaluation. Can represent broad markets or single sectors. Calculated by exchanges and mimicked in mutual funds and ETFs.

Stock Indexes - Types

DJIA (Dow Jones Industrial Average): Price-weighted index. NASDAQ: Market or value-weighted index. S&P 500: Market or value-weighted index.

Price-Weighted Index - Calculation

Formula: Index = (Price of Stock A + Price of Stock B + Price of Stock C) / Divisor. Example: Stock A: $10.50, Stock B: $50, Stock C: $85. Index = ($10.50 + $50 + $85) / 3 = $48.50. Adjustment for Stock Splits: If Stock C splits 2:1, the new price is $42.50, and the divisor is adjusted to maintain the index value.

Stock Splits - Impact

A stock split increases the number of shares outstanding while reducing the price per share, maintaining the overall market capitalization.

2:1 Split

Shareholders receive two shares for each share owned, and the share price drops to half.

4:1 Split

Shareholders receive four shares for each share owned, and the share price drops to a quarter.

No Change in Firm Value

The total value of the firm remains the same; only the number of shares and price per share change.

Apple Stock Split 2020

4:1 split (its fifth split).

Tesla Stock Split 2020

5:1 split.

Amazon Stock Split 2020

Proposed a 10:1 split in 2020 but decided not to.

Amazon Stock Split 2022

20:1 split, making shares worth $7.70 each.

Reverse Split

Combines shares to increase the price per share.

1:10 Reverse Split Example

A 1:10 reverse split would combine 10 shares into 1, increasing the share price tenfold.

Purpose of Reverse Stock Splits

Often used to avoid delisting from exchanges due to low share prices.

Value-Weighted Index Formula

Index_t = Index_t-1 × (∑V_t / ∑V_t-1)

Total Value Calculation Example

Total Value on Sept 24: $163,500

New Total Value Calculation Example

New Total Value: $135,000

Index Calculation Example

Index on Sept 25 = 100 × ($135,000 / $163,500) = 82.569

HPR Example

HPR: -17.43%

Price-Weighted Index

Stocks with the highest price have the most influence (e.g., Stock C in the example).

Value-Weighted Index

Stocks with the highest market value have the most influence (e.g., Stock A in the example).

Price-Weighted Index Example

In the given example, the price-weighted index lost 8.74%.

Value-Weighted Index Example

In the given example, the value-weighted index lost 17.43%.

Short Selling Process

1. Borrow shares from a broker (e.g., Jill). 2. Sell the shares at the current market price (e.g., $25). 3. Wait for the price to drop (e.g., to $20). 4. Buy back the shares at the lower price and return them to the broker. 5. Profit: $5 per share (minus commissions).

Short Selling Restrictions

The short seller must pay any dividends issued while the shares are borrowed.

Delivery Requirement in Short Selling

The short seller must deliver the shares back to the lender when requested.

Short Covering Rally

Short sellers buy back shares to lock in profits, causing the price to rise.

Short Squeeze

A rapid increase in stock price forces short sellers to buy back shares to cover their positions, further driving the price up.

Margin Trading

Borrowing money from a broker to buy securities.

Margin Trading Example

Buying $100 worth of stock with $50 of your own money and $50 borrowed from the broker.

Leverage in Margin Trading

Amplifies both gains and losses.

Margin Call Formula

Margin Call Price = (Amount Owed) / (1 - Maintenance Margin)

Margin Call Example

If you owe $50 and the maintenance margin is 35%, the margin call price is $76.92.

Margin Call Explanation

If the stock price drops to $76.92, you must either add funds or sell the stock to maintain the required margin.