Risk And Return I Flashcards
Holding period return
[(1 + r ) (1 - r) … ] -1
Annualized return in HPR function formula
Geometric mean of Holding Period Return
[(1+ HPR) ^ 1/n ] -1
How to calculate Money Weighted Return? 3 steps
Consider all inflow and outflow
- Identify inflows and outflow’s (be careful with dividends. If they are not reinvested, INFLOW)
- Draw the flows
Net Cash Flows = CF0, CF1, CF2…
- Calculate IRR
Regarding Trading costs, liquidity is least like to affect
Brokerage commissions
(Fixed costs negotiated with brokerage firm)
The relationship of risk aversion and risk return is negative, positive or neutral ?
Positive
Utility Function and cofficient A analysis
U = E(r) - 1 A (desvPad) ^ 2
—-
2
U = utilities
E(r) = Expected return
A = measure of risk aversion
DesvPad ^ 2 = Variance of the investment
A > 0 —> risk aversion
A = 0 —> neutral
A < 0 —> Risk taker
CAL - Capital Allocation Line
Formula
Considerations
(Rf)
E(Rp) = Rf + (E (ri) - Rf ) desvP
————————-
Desv i
Cal represent the ser of all feasible investments
PLOT Rf + Risky assets
Differents investors of differents risky assets, combining with RF must lie on CAL
StndDev of portfolio formula
[(Wa )^2 x (DesvPad a ) ^2
Same for Asset B
+
2 WaWbDesvpadADesvpadB
ALL ^ 1/2
Correlation = ? Formula
COV 1,2
————-
DesvP1 DesvP2
Covariance formulas (2)
(R1 - Rbar) + (R2 - Rbar)
——————————-
N-1
Cov 1,2 = correl (std1) (std2)
What is the value of correl (rô) of assets uncorrelated?
Zero
Relation about Risk aversion and Indifference curve (slope)
More risk averse, more slope
Risk averse people need more return per unit of risk (greater slope)
Risk taker will not demand excessive return for risk
Variance of equally weighted portfolio Formula:
(What happens to the contribution of individual asset for volatility if we ADD more assets)?
Vol^2 = vol avg^ 2 + N -1 (cov avg)
—————. ———
N. N
Contribution of each asset DECREASES
Contribution for COV AVG n CORREL INCREASE
What is the efficient frontier?
All attainable risky assets
With
Highest expected return
For a given level of risk
What are the Minimum Variance Frontier
And global minimum Variance portfolio:
Minimum Variance Frontier =
difference between Efficient frontier
and the surplus amount of risk
Global minimum variance portfolio =
1.“safest” portfolio of the frontier.
2. Bunda da Markowitz efficient frontier.
3. Left most off all portfolio risky
What type of porfolio most fits with risk- neutral investor?
More return possible.
Remember: U = E(r) - 1/2 x A (zero) StdDev
So U = E(r)
Why dominant CAL (Capital Allocation Line) has a Higher Rate of Return for levels of risky greater than
Optimal portfolio ?
Hability to borrow at the Rf rate
(i.e Buying on margin)
Time weighted rate of return formula step by step ( look for the period. If are greater than 1, GEO MEAN)
- Sub periods of adds or withdrawals (dividends, etc)
- HPR for all subperiods
3.[( 1+HPr1 ) (1+HPRn) ] -1
ATTENTION
If the total investment period is greater than 1, geometric mean
What is the name of The point which tangency the CAL and efficient frontier is:
Optimal Risky Portfolio
Draw of the value of A and the risk profile (risk aversion) - term in Utility Formula-
(The A stands in the central)
Taker<————A ————> Averse
Neutral
