Asset Classes and Financial Instruments

Real Assets Versus Financial Assets Real Assets Has productive capacity Financial Assets

• Claims on real assets
  • Do not directly contribute to productive capacity
  • Fixed-Income Securities
  • Equity
  • Derivatives
• Other Investments
  • Currency
  • Commodity and derivative markets
• Financial Markets and the Economy
  • Informational role
  • Collective judgment determines stock prices
  • Consumption timing
  • Separate decisions concerning that otherwise would be imposed by current earnings
  • Allocation of risk
  • Risk preferences
• Agency Problems
  • Tying compensation to stocks
  • Monitoring from board of directors
  • Monitoring from large investors and security analysts
  • Takeover threat for poor performers
  • Takeover threat for poor performers Financial Markets
  • Money Market
  • Short-term securities (< 1 year)
  • Capital markets
  • Long-term bond
  • Equity markets
  • Derivative markets
• The Money Market
  • T-Bill Yields
    • Bank-discount method
    • Based on par value (Face value) as a denominator and 360 days I a year
    • Bond-equivalent yield
    • Yield is computed based on current price or the purchase price as a denominator and 365 days in a year
• Commercial paper
  • Bonds issued by highly rated companies Bankers’ Acceptances
  • Second only to T-bills in terms of default security
  • Canadian Dealer Offered Rate (CDOR)
  • Bank guarantees that the debt obligation will be fulfilled
  • Inflation-Protected Bonds – TIPS or RRB
• Taxable vs. Tax-Exempt Bonds r * (1-t) > rm
  • rm: municipal bond rate Corporate Bonds
  • Semi-annual interest payments
  • Callable
  • Issuer can exercise the call option to buy the bond back
  • Poisoned put
  • Forces takeover to buy the bond
  • Retractable and extendible
  • Modifying the maturity date
  • Convertible
  • Bond holder can convert bond to equity
• Common Stock eQuity
  • Residual claim
  • Limited liability
• Dividend yield
  • Annual dividend / stock price as a percent
• Capital Gains
  • P – C

P-E ratio

What is should be versus what it is. Payout ratio over (ke – g). Or (1- retention ratio) / (ke – g) = (1-r)/(k_f+β(mrp)-g)

Sustainable growth: based on what is retained, times the return on earnings?

ROE = Earnings / Book Value

Preferred Stocks

Cumulative means that missed payments are still owed. With non-cumulative preferred shares, company does not have to pay the missed payments ever.

Shares become voting at default payment to preferred shares

• Income Trusts

  • Usually stable revenues

• ADR

  • American Depository Receipts
  • Trade foreign companies within the USA

• Indexes

  • S&P/TSX
  • S&P/TSX 60 Index
  • S&P/TSX MidCap and SmallCap
  • S&P/TSX Venture Index

• The DOW is price-weighted and not value weighted.

• Futures vs. Options

  • Future: obligation, option: right

Securities Trading

How Firms Issue Securities

• Initial Public Offerings
  • Road show to publicize new offering
  • Bookbuilding to determine demand
  • Degree of investor interest provides valuable pricing information
  • Underwriter bears price risk
    • IPOs are commonly underpriced
      • Twitter
    • Some IPOs are well overpriced
      • Facebook
        • Retail investor interest lasts only for 2 days. Institutions always drive volume

over-allotment: when all equity is sold so banks want more to sell

underwriter takes the risk

Types of Orders

• Market order: buy or sell
• price-contingent order:
  • Limit buy (sell) order to buy at below (above) specified price
• large order filled at multiple prices

Trading Strategies

• Algorithmic trading
• High-frequency trading
  • HIgh volume low profit
• Dark pools
  • private trading systems in which participants can buy or sell large blocks of securities without showing their hand

Trading Costs

• Explicit cost
  • Commission
• Implicit costs
  • Dealer’s bid-ask spread
  • Price concession an investor may be forced to make for big quantities
  • Buying board lots is prioritized than fractional

Trading with Margin and Short Sales

• Initial margin is usually 50%

  • Maintenance margin
  • When equity is 30%, add more money
  • How far can a stock price fall before a margin call?

• P = Purchase Price * (1 - initial margin) / (1 - maintenance margin)

• equity required = initial margin * value - value + borrowed = 1,800

• equity total required = 0.6 * value

Leverage

Multiplier effect

Short Sale

Benefit when price goes down.

Insider Trading

• Someone trading on information not profitable
• Most common is spouse of someone on legal team

Questions

A t-bill has a bank discount yield of 6.81% based on teh ask price and 6.9% based on the bid price. The maturity of the bill is 60 days. Find the bid and ask prices of the bill.

Convert 6.81% and 6.9% for 60 days. 360 days in a year

• 1000 - 1000 * 0.0681 * 60 / 360 = 988.65
• 1000 - 1000 * 0.069 * 60 / 360 = 988.5
• Therefore the bid-ask spread is just $0.15

A u.s. treasury bill with 90-day maturity sells at a bank discount yield of 3%.

a. what is the price of the bill? b. what is the 90-day holding period return of the bill? c. what is the bond-equivalent yield of the bill? d. what is the effective annual yield of the bill

Purchase 300 shares of GameStart at $40/share. Borrows $4,000 from her broker to help pay for the purchase. Interest rate on loan is 8%.

a. What is the margin of Dei’s account when she first purchases the stock? b. share price falls to $30 per share, what is the remaining margin (equity) on the account? c. margin requirement is 30%, will a marign call occur? d. What is the rate of return?

Short sell 1000 shares of GameStart at $40 per share. Initial margin was 50%. Price rose $10. Stock paid dividend of $2.

a. What is remaining margin? b. 30% margin requirement c. rate of return?

Consider the following limit order. The last trade was at $50.

….

a. market buy for 200 shares, what price will it be filled at? b. at what price would the next market order be filled?

Investment Companies

• Mutual funds
  • Record keeping and administration
  • Pool everyone’s money and invest
  • Professional management
  • Lower transaction costs
  • Net Asset Value (market value - liabilities over shares outstanding)
• Unit investment trusts
• REITS
  • Real Estate Investment Trusts
• Hedge funds
  • Private investors pool assets to be invested by fund managers
• Closed-end funds
  • Do not redeem or issue shares
  • Constant shares outstanding
  • Investors cash out by selling to new investors
  • Priced at premium or discount to NAV
• Open-end
  • Stand ready to redeem or issue shares at NAV
  • Priced at Net Asset Value

Mutual Fund Investment Policy

• Money market funds
  • Invest in money market securities such as commercial paper, repurchase agreements, or CDs
• Equity funds
  • Invest primarily in stock
• Sector funds
  • Concentrate on a particular industry or country
• Bond funds
  • Specialize in the fixed-income sector
• International funds
  • Global and emerging market
• Balanced funds
  • Designed to eb candidates for an individual’s entire investment portfolio
• Asset allocation and flexible funds
  • Hold both stocks and bonds
  • Engaged in market timing; not low-risk
• Index funds
  • Tries to match the performance of a broad market index
• Liquid alternatives
• ESG funds
  • screened against environmental, social, and governance factors

Fee Structure:

1. Management Fees and Operating Expenses
2. Front-end load
3. Back-end load
4. Trailing Commissions

Exchange Traded Funds

• Mirrors an index
• Trades like a stock
• Lower costs
• Tax efficiency

Hedge Fund Strategies

• Directional
  • Bets that one sector or another will outperform other sectors
• Non-directional
  • Buy one type and sell another
  • market neutral
• Statistical arbitrage
  • etc

High-Frequency Strategies

• Electronic news feeds
• Cross-market arbitrage
• Electronic market making
• Electronic “front running”

Examples

1. An open-end fund has a net asset value of $10.70 per share. It is sold with a front-end load of 6%. What is the offering price?

• $10.70 after offering price, so offering price = 10.70 / 0.094 = 11.38

2. The offering price is 12.30 with a front-end load of 5%. What is the NAV? NAV = 12.30 * 0.95 = $11.69

3. You purchased 1,000 shares at $20 with a front-end load of 4%. Securities increased in value by 12%. There is a 1.2% expense ratio. What is the rate of return?

OFF = 20 / 0.96 = 20.83

Final value = 20 * 1.12 * (1 - 0.012) = 22.13

Rate of return = 22.13 / 20.83 - 1 = 6.24%

4. Loaded-up fund has an expense ratio of 1.75%. Economy Fund has a front-end load of 2% but an expense ratio of 0.25%. Assume rate of return is 6% before any fees.

• LU = 1000 * 1.06 * (1 - 0.0175) = 1041.45 -> 4.1%
• EF = 1000 * (1 - 0.98) * 1.06 * (1 - 0.0025) = 1036.20 -> 3.62%

Risk & Return

• Rate of return on zero-coupon bond; r = (100/Price) - 1
  • r = (FV/PV)^(1/m) - 1
• Annual Percentage (Posted) Rate (APR)
• Effective annual rate (EAR):
  • Takes into consideration the effects of compounding
  • (1 + APR/n)^n - 1
  • Example
    • APR of 4.5%, m = 4
    • 100((1 + 0.045/4)^4 - 1) = 4.58%
    • What if you want 4.58%?
    • Bank A: 4.58% APR, m = 1
    • Bank B: 4.5%, m = 4
    • Bank C: APR if compound is 12?
      • 12 * (1.0458 ^ (1/12) - 1) = 4.4867%
    • Continuous compounding
      • FV = euler’s constant ^ (rt)
      • For a EAR of 4.58%, ln (1 + 4.58%) = r -> r = 4.475%

Interest Rates and Inflation Rates

• Nominal rate is the growth of your money = 11.5%

• Next year, you get 1.115

• Coffee is $1 today, but given an Average annual rate of inflation of 3.5%, the coffee will be 1.035.

• You could buy 1 coffee now and 1.077 next year

• Change in purchasing power = return return = 1.077 / 1 - 1 = 7.7%

• Fisher equation: N approxEqal to real return + inflation

• Return = (1 + N) / (1 + inf) - 1

• Equilibrium rate of return

RIsk and Risk Premium

• Holding Period Return = (enter price - enter price + dividend) / (enter price) = Capital Gain Yield + Dividend Yield
• E(r) = sum of probability of state + return if state occurs
• Variance:
• Standard Deviation (STD)

• STD = sqrt(0.038) = 19.49%

• Based on a normal distribution, we can expect a return of 9.76% +- 19.49% 68% of the time.

• Risk: likelihood of something happening and magnitude

• STD gives us both the magnitude and the likelihood

• Look at historical returns, and calculate the STD of those returns to get the

• Skewness: positively skewed means a tail on the right

• Kurtosis: how normally distributed data is (fatness of the curve)

Calculating the STD of a Stock Tutorial

1. Download monthly data for 5 years from yahoo finance
2. Keep only date and adjusted Close columns. Adjusted close factors dividends.
3. Make a column called r and use the formula (=X4/X3-1)
4. Calculate average of the rates
5. Create a column called variance and use the formula (=(X3 - $AVERAGE$RATE)^2)
   • Or use the VAR formula in Excel
6. Calculate the variance which is the SUM of the column divided by the number of rates MINUS 1
   • In a sample, 1 is subtracted to remove the bias to the mean
7. Square root the variance to ge the standard deviation of the monthly return
8. You can skip the manual calculations and use the VAR and STD formulas provide by Excel.
9. You can get the SKEW of the data by using the SKEW function on the returns
10. Manually calculating the SKEW
    • Create a column and instead of squaring the deviation, cube it
    • Divide by the number of rates MINUS 1, and then multiply by the standard deviation cubed
11. Use =KURT to get the kurtosis of the rates
    • 3 is NORMAL
    • The lowe the Kurtosis the tighter in the middle

Risk Measures

• Value at risk
  • Loss that will be incurred in the event of an extreme adverse price change change with some given, usually low, probability. Typically, use 1st percentile
  • -2.33 STD
  • 9.76 - 2.33 * 19.49 = -35.65%
• Expected Shortfall (ES)
• Lower partial standard deviation (LPSD)

Capital Allocation

• Risk-averse investors consider only risk-free or speculative prospects with positive risk premiums
• Portfolio is more attractive when its expected return is higher, and its risk is lower
  • what happens when risk increases along with return

Utility Values

• U = Utility Value
• E(r) = Expected return
• A = Index of the investor’s risk aversion
• Variance of returns
• Scaling factor of 0.5 (half year)

Investor Types

• Risk-averse: want compensation for risk via a premium. A > 0;
• Risk-neutral; A =0
• Risk-lovers; A < 0

Mean-Variance Criterion

• E(rA) >= E(rB)
• STD_A <= STD_B

Capital Allocation Across Risky and Risk-Free Portfolios

• Manipulate the % invested in risk-free vs risk portfolio

Total market value: $300,000, risk-free: $90,000.

• Equities: 113,400
• Bonds: 96,600

90 day T-bill is considered the risk-free asset.

One Risky Asset and a Risk-Free Asset Portfolios

• Reward-to-volatility ratio (aka Sharpe ratio)
  • Excess return vs. portfolio standard deviation

y* = ( E(rp) - rf )/ A std^2 = 41.3%

Indifference curves + Capital Allocation Line

To find the weighting to invest in the risky and risk-free portfolio.

Now we get optimal allocation for any portfolio.