Return, Risk and Diversificiation Flashcards
Week 3
What is Risk? What is the issue with risk and attitudes?
- Risk is how you choose between different assets- to hold an asset you expect a return
- Risk is symmetrical; +ve higher return than expected, -ve lower than expected return
- Attitudes are asymmetrical; we tend to be risk-averse (worrying about the downside more) but it isn’t linear
What is Risk Aversion?
- If two assets have the same expected return, you will take the less risky one
- For individuals to hold riskier assets, they must be compensated with a greater return
How much more did company stocks return that treasury bills?
- 5x (1925-2007)
How is risk priced?
- Risk premium (stock x return - treasury bill return)
- This gives you a fairly large number, as treasury bill is seen as riskless
What is the average return over time? What does that then make risk?
- Ṝ = 1/N ΣRt
- Average Return = Unrealised
- Actual Return (Rt) = Realised
- Risk is, therefore, the difference between the average return and the actual return
What is the formula for the Variance of the Return?
- Var (Rt) = σ² = 1/N-1 [Σ(Rt - Ṝ)²]
What is Mean-Variance Analysis?
- Suggests that investors will always prefer portfolio x for a maximum return given a specific variance OR a minimum variance given a specific return
- E(R1) < E(R2) & σ²(R1) ≥ σ²(R2)
- E(R1) > E(R2) & σ²(R1) ≤ σ²(R2)
How are returns distributed? Is it an approximation?
- Returns are normally distributed
- Probability of x+/-σ = 68%
-Probability of x+/-2σ = 95%
-Probability of x+/-3σ = 99% - Bell-curve describes the probability to end up in a given range (describes σ² and μ)
- This is only an approximation so should only be taken as an estimate
How is risk and return calculated?
- E(R) = R hat =ΣRipi
- σ² = Σpi(Ri-Ṝ)²
What are more definitions concerning portfolios and diversification?
- Portfolio = A group of assets held by an investor
- Portfolio weight = The percentage of a portfolio’s total value that is in a certain asset
- Diversification = Investing in different assets in an attempt to reduce overall investment risk to avoid big losses for a single asset
How many different assets are optimal to invest in for a diverse portfolio and to reduce specific risk?
- 10 - 15
What is the difference between specific (unsystematic) and market (systematic) risk?
- Specific risk is the risk that a certain asset holds (CAN BE eliminated through diversification)
- Market risk is the risk that the whole market has (CANNOT BE eliminated)
What is diversification? When are the benefits the highest?
- Reduces risk/variability by spreading out funds in different assets
- The most dramatic effect in risk reduction comes in the earliest stages of diversification
What is Covarience? How does it differ from Correlation? What are the formulas?
- Covariance = sum of deviations of assets, measures how much variables change
- Cov(x,y) = E[(x-E(x)) - (y-E(y))] = 1/N-1Σ(x-E(x))(y-E(y))
Correlation = Measures how related assets are - ρxy = Cov(x,y)/σ(x)σ(y)
Prove the Variance of an Asset
- σ²(Rp) = E[Rp-E(Rp)]²
Assuming two assets, R1 with weight ω1and R2 with weight ω2: - σ²(Rp) = E[(ω1R1+ω2R2) - (ω1E(R1)+ ω2E(R2))]²
Factoring out ω1 and ω2, - σ²(Rp) = E[ω1(R1-E(R1)) + ω2(R2-E(R2))]²
Using (a+b)², - ω1²σ²(R1) + ω2²σ²(R2) + 2ω1ω2E[(R1-E(R1))(R2-E(R2)]
As σ² = (R1-E(R1))², - σ²(Rp) = ω1²σ²(R1) + ω2²σ²(R2) + 2ω1ω2Cov(R1,R2)
Rearranging ρxy = Cov(x,y)/σ(x)σ(y), - σ²(Rp) = ω1²σ²(R1) + ω2²σ²(R2) + 2ω1ω2 ρR1R2 σ(R1)σ(R2)
