What is the SAA?
The Stategic asset allocation determines target allocation for different asset classes. Evey Period the portfolio will be rebalnced to its original allocation
What types of possible investment classes exist?
When do we use the geometric mean and the arithmetic mean?
Buy and Hold -> Geometric Mean
Rebalancing -> Arithmetic Mean
What does a high Risk Premium implies in the CAPM or the Multifactor Model?
A high Risk Premium implies that the stock, wether in the CAPM oder multifactor models, with high betas are risky. Because if the Market (CAPM) oder the Factor (Multifactor) is facing a bad time, the single stock will have low returns.
What can we summerize, if the payoff of an asset tends to be as followed
high in bad times
low in bad times
High in bad times -> valuable asset to hold -> low expected return
Low in bad times -> risky asset to hold -> high expected return
How should we value assets during low consumptions?
If the assets payoff, thes are valuable assets -> low expected return
Why does equity peform badly in the short run, if we are in a high inflation periods.
High inflation -> low growth
Money illusion -> Investors use nominal discount rate instead of real discount rate
Why should in the dynamic portfolio choice the periodic weights of an allocation change, during investing in the long run?
The dynamic portfolio choice states, that at every period the variables for an investors change.
What are the solutions for the dynamic portfolio choice?
The solution is the “dynamic programming” or “control problem”.
We slice a long horizon problem into a series of one period problems and make a backward iteration.
Now we have a series of one periods, so the long run inverstors are just like short term invesotrs.
How does the “dynamic programming” or “control problem” solution work?
We will look backwards at our horizon.
What is the benefit from the “dynamic programming” or “control problem” strategy?
The dynamic strategy is completly known, even though it changes over the time.
Utilty could change
Returns could be predictiable
And the strategy will optimally response
What is the “Time diversification fallacy” by Samuelson.
How does this affect the losses?
Risk does not diversify over time, instead risk increases proportional over time.
Our potential losses increases.
What das the “Myopic” portfolio choice tells us in terms of risk and the investment horizon, iff the i.i.d. holds?
Under the i.i.d., the optimal portfolio is independent of the investment horizon.
Long Run = Short-Run
How does the Buy and Hold Strategy differes from the perspective, that long-term investors should behave like short-term investors?
The Buy and Hold investors does not rebalance his portfolio.
What is the “fallacy of large numbers”?
If we have infinite time, the shortfall risk goes to zero. But the average loss in the case of a default increases. So Risk does nit diversify with time nor splitting the money over independent investments.
We invest the same amount of money repeadetly and cumulating the risk
What happens, if returns deviate from the i.i.d. assumptions and are predictiable in terms of the mean and the variance?
High Returns today implies high returns tomorrow
High Returns today implies low returns tomorrow
The Mean and the Variance do no longer scale with the horizon. For example:
High Return today implies high return tomorrow, the variance will increase with horizon faster that the mean -> Stocks are worse for long run
High Return today implies low return tomorrow, the variance of long horizon is lower thant variance of one period times the long horizon-> Stocks are mor attractive
What happens, if return are predicitable in terms of weights?
The static portfolio weight changes every period. These Weights are called “myopic weights”
What is the optimal weight in a opportunistic strategy?
How can we interpret the formula?
Optimal weight = Myopic weights + Hedging demand
One Period Solution (TAA)
Hedging demand weight
Takes advanteges of the long horizon for predictable returns and hedges against changes in the investment opportunities (SAA)
What is the main intuition of the Hedging demand?
Equities provide a hedge against theier own risk. If prices drop -> Expected Values are high.
How does the hedging demande behave, if the horizion increase?
It increases with the time horizon. It is like a leverage
What does Campbell and Viceira do in their study? What do they show in their study?
The Model that investors desire life consumption rather than portfolio return at a fixed terminal horizon.
The find out, that failing to time the market could lead to large costs in terms of the utility
Which Rebalance strategies exists?
Periodic Rebelancing (No matter what happens, you always rebalance)
Range Rebalancing (You only Rebalnce, if the weights reached a certain range)
Most Important thing is to rebalance
What is the Constant Mix (Rebalancing)
Investment in Stocks as a prportion of Wealth.
Sell Stocks when the arise, buy stocks when they fall
Define the “cushion” in the Constant Proportion portfolio insurance
It is the difference between Portfolio Value and NPV of the floor.
How does the constant proportion portfolio insurance work?
As long as the investor can tolerate the loss. We will adjust daily our portfolio.
Calculate NPV of Floor
Calculate the cushion
With the Cushion and our multiplier we can calculate our portfolio weight.
As long as we dont hit the NPV Floor with losses, we adjust our portfolio
How do we behave in the CPPI, if stock prices are rising or falling.
We will sell, if they fall and we will buy, if the rise. It is a Convex strategy
Why cant everybody rebalance his portfolio?
Because the average investor holds the market portfolio
The Market Portfolio itself is Buy and Hold
How is our risk aversion during
During bad times, risk aversion could be very high
Equities perform bad
During good times, risk aversion is very low
Equities perform well
How the long run investor favorable against the short run investor in the dynamic programming?
Because the behave same, the longrun investors has the advatage from the time horizon.
What das Samuelson (1969) state and what are the necessary assumptions?
He states, that the Expected utilty does not increase with a higher fraction of risky assets with increasing time horizon.
Constat RRA, percentage of risky assets does not change regardless of the wealth
Returns are indipendent and random
The Dynamic Portfolio problem becomes a series of identical one-period problems
How does an investor weight his portfolio, if the i.i.d assumotions dont hold.
The Investor will change his portfolio every weight.
Does Equity have premium in terms of consumption?
Yes, because equity covaries with consumption. If Consumption is low, returns of equity are low -> premium is needed to compesate the bearing risk
What is the standpoint of Mehra and Prescott in terms of the relationship of equity premium and consumption?
What are their reasons?
Eventhough there is a low conumption, with a reasonable risk aversion the risk premium should be below 1%.
The reasons are
Equity volatility is far higher thant consumption volatility
Equity returns are lowly correlated with consumption growth
What is the “hedging demand” in the Oportunistic strategy?
A Investor take advatages from the long time horizon and use predictable returns to hedge against changes in the investment opportunity
What is the liability hedge?
The liability hedging portfolio is a portfolio with a high correlation with the liabilites. The Portfolio is there to ensures the liabilites are met. It is the true “risk free asset”.
Discuss how a higher fraction of stocks (relative to the risk-free asset) might be justified in the long run if returns are predictable
In the long run- investors are leveraged short run investors. They Hedge and the hedge demand increases with the time horizon. Equity is a hedge in itself. If equity prices drop, the excpected return increases. If the expected returns are high, long investors will buy even more equity.
Why is it importnt to understand why the equity risk premium exists?
For our understanding wether equities have high returns in the future
Recommending an optimal asset allocation
What is the correlation between excess stock returns and inflation?
They have a low correlation, sometimes even negative
How should we rebalance our portfolio, if the stock returns are predictable?
We should even invest in more stocks than the rebalancing demand