Lecture 1 - Risk & Return Flashcards
What is portfolio management?
Determining the mix of assets to hold in a portfolio
Asset Classes
- Stocks
- Bonds
- Cash
- Real Estate
Non-Traditional Asset Classes
- Options, Derivatives, Futures
- Commodities
- Hedge Funds, Private Equity
What is a 60/40 portfolio?
- 60% Equities
- 40% Bonds
Portfolio Strategies
Active & Passive
Active Portfolio Manager Goal
Beat an index
Passive Portfolio Manager Goal
Maintain index return
Factors Influencing Interest Rates
- Supply
- Demand
- Government’s Net Supply/Demand
- Expected Rate of Inflation
Correlation between interest rates & fund supply
- As interest rates increase, fund supply increases because people are willing to lend money due to high interest rates
Correlation between interest rates & fund demand
- As interest rates increase, fund demand decrease because borrowing becomes more expensive
Nominal interest rate = ?
R
Real interest rate approximation formula = ?
r = R - i, where i = inflation
Real Interest Rate Formula = ?
r = (R - i)/(1 + i) - 1
HPR Meaning
Holding Period Return
HPR Formula #1 = ?
HPR = (P1 - P0 + D1)/P0
HPR Formula #2 = ?
HPR can either be nominal or real so you would use the nominal/real interest rate formula
Expected Return Formula
E(r) = Σ p(s)r(s)
Variance (VAR) Formula
σ^2 = Σ p(s) x [r(s) - E(r)]^2
Variance (VAR) Formula if no probabilities are given
σ^2 = 1/n Σ [r(s) - r (mean)]^2
Standard Deviation (STD) Formula
√σ^2
Excess Return
The difference in between the actual rate of return on an asset and the actual risk-free rate
Risk Premium
The difference between the expected HPR on a risky asset and the risk-free rate
Sharpe Ratio
Sharpe Ratio = (Expected Portfolio Return - Risk Free Rate)/Standard Deviation of Portfolio
Risk Measures
- Value at Risk (VaR)
- Expected Shortfall (ES)
- Lower Partial Standard Deviation (LPSD)
- Sortino Ratio
Value at Risk (VaR)
Measure of downside risk. The loss that will be incurred in the event of an extreme price change.
Expected Shortfall
The expected loss on a security conditional on returns being in the left tail of the probability distribution.
Another term known as expected shortfall is…..
Conditional Tail Expectation
Lower Partial Standard Deviation
Uses only negative deviations from the risk-free return
Sortino Ratio
Sortino Ratio = (Expected Portfolio Return - Risk Free Rate)/LPSD
Intrinsic Value
Value calculated for equities using a specific model
Market Price
Current price of the stock
IV > MP means?
Buy
IV < MP means?
Sell or Short
IV = MP means?
Hold or fairly priced
Three Cases of DDM
1) No Growth DDM
2) Constant Growth DDM
3) Multi-Stage DDM
No Growth DDM Formula
P0 = DIV1/r
Note* DIV can also be EPS
Constant Growth DDM is also known as the……..
Gordon Growth Model
Constant Growth DDM only works when?
r > g
Constant Growth DDM Formula
P0 = DIV1/r-g
or
P0 = DIV0 (1 + g)/r-g
If the dividend is just paid for constant growth DDM, what formula do you use?
P0 = DIV0 (1 + g)/r-g
If the dividend is paid at the end of the year or is next years dividend for constant growth DDM, what formula do you use?
P0 = DIV1/r-g
What is the current price of a 7% coupon bond, paying semi-annually with 3 years to maturity, if market interest rates are 5%? The face value of the bond is $1000.
I/Y = 5%/2 = 2.5%
PMT = $1000/2 x (0.07) = $35
n = 3 x 2 = 6
FV = 1000
CPT PV = $1055.08
What would your rate of return be if you purchase a 5-year bond paying an 8% coupon at $1,035 and sell it one year later when its yield to maturity drops to 6.2%? Assume the coupons are semi-annual and not reinvested.
Step 1: Find PV
PMT = 1000 x 8% = 80/2 = $40
FV = 1000
n = 4 x 2 = 8
i = 6.2%/2 = 3.1%
CPT PV = -$1062.91
Step 2: Find Rate of Return over holding period
Rate of Return = (Coupon Interest + Price Change) / Initial Price
Rate of Return = ($40 x 2 + ($1,062.91 - $1,035)) / $1,035 = 10.4262%
Step 3: Find Annual Rate of Return
Since there is a one year holding period, EAR = 10.4262%
What was your one-year rate of return if you purchased a bond in 2022 at a 2% YTM and then sold it one year later when YTM increased to 4%? Assume a 2% coupon (paid semi-annually, 10 years to maturity (at purchase), par value $1000.
Step 1: Find PV
FV = 1000
PMT = (2% x 1000)/2 = $10
N = 20
i/y = 2%/2 = 1%
CPT PV = -$1,000
Step 2: Find selling price after one year
FV = 1000
PMT = $10
N=18
i/y=2%
CPT PV = -$850
Step 3: Find HPR
HPR = (Ending Price - Begin Price + CFs)/Beginning Price
HPR = (850 - 1000 + 20)/1000 = -13%
Briefly explain why the 60/40 portfolio often has performed well for investors historically
Historically, stocks and bonds have proven to have a negative correlation. Combining assets with negative correlations provide portfolio managers with the best risk-return combinations.
Why didn’t bonds help the 60/40 portfolio as a “diversifying” asset class in 2022
Since central banks cut interest rates to support the economy. When banks ease policy, bond yields drop and bond prices rise
