# BU 473 Investment Mangement

## 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

- T-Bill Yields
- 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
- Some IPOs are well overpriced
- Facebook
- Retail investor interest lasts only for 2 days. Institutions always drive volume

- Facebook

- IPOs are commonly underpriced

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

## answer

a. 1000 - 1000 * 0.03 * 90 / 360 = 992.5 b. 1000 / 992.5 = 0.756% c. 365 days instead of 360: yield = (1000 - 992.5) / 992.5 * 365 / 90 = 3.06% d. 1.00756 ** (365/90) - 1 = 3.1%

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?

## answer

a. (300 * 40 - 4,000) / 300 * 40 = (12,000 - 4,000) / 12,000 = 66.7% b. 4000 * 1.08 = 4680 c. 4680 / 9000 = 48% > 30%, so no d. (4680 - 8000) / 8000 = -41.50%

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?

## answer

a. Initial equity is 50% * 4,000 = 20,000. Final equity is 20000 + (40 - 50 - 2) * 1000 = 8,000 b. 8000 / (50 * 1000) = 16%, so yes c. (8000 - 20000) / 20000 = -60%

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:

- Management Fees and Operating Expenses
- Front-end load
- Back-end load
- 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

- 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

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

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%

- 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)

State | Prob. of State | r in State | Weighted r | Var |
---|---|---|---|---|

Excellent | .25 | 0.3100 | (25)(.31) | (3.1% - 9.76%)^ (.25) |

Good | .45 | 0.1400 | (.45)(.14) | (14% - 9.76%)^ (.45) |

Poor | .25 | -0.0675 | (.25)(-0.0675) | (6.75% - 9.76%)^ (.25) |

Crash | .05 | -0.5200 | (.05)(-.52) | (-5% - 9.76%)^ (.05) |

Total | 1 | N/A | 9.76% | 0.038 |

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

- Download monthly data for 5 years from yahoo finance
- Keep only date and adjusted Close columns. Adjusted close factors dividends.
- Make a column called r and use the formula (=X4/X3-1)
- Calculate average of the rates
- Create a column called variance and use the formula (=(X3 - $AVERAGE$RATE)^2)
- Or use the VAR formula in Excel

- 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

- Square root the variance to ge the standard deviation of the monthly return
- You can skip the manual calculations and use the VAR and STD formulas provide by Excel.
- You can get the SKEW of the data by using the SKEW function on the returns
- 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

- 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.