Investing for the Long Run

The Stategic asset allocation determines target allocation for different asset classes. Evey Period the portfolio will be rebalnced to its original allocation

• Expected Returns

• Risk tolerance

• time horizon

• Traditional

  • Bonds

  • Stocks

• Alternative

  • Real Estate

  • Private Equity

• Buy and Hold -> Geometric Mean

• Rebalancing -> Arithmetic Mean

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.

• High in bad times -> valuable asset to hold -> low expected return

• Low in bad times -> risky asset to hold -> high expected return

• If the assets payoff, thes are valuable assets -> low expected return

• High inflation -> low growth

• Money illusion -> Investors use nominal discount rate instead of real discount rate

He doesnt buy and hold, he constantly is buying and selling

The dynamic portfolio choice states, that at every period the variables for an investors change.

• Investment Opportunities

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.

We will look backwards at our horizon.

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

Risk does not diversify over time, instead risk increases proportional over time.

Our potential losses increases.

Under the i.i.d., the optimal portfolio is independent of the investment horizon.

• Long Run = Short-Run

The Buy and Hold investors does not rebalance his portfolio.

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

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

The static portfolio weight changes every period. These Weights are called “myopic weights”

If mean and volatility are constant:

Optimal weight = Myopic weights + Hedging demand

• Myopic Weight

  • 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)

Equities provide a hedge against theier own risk. If prices drop -> Expected Values are high.

It increases with the time horizon. It is like a leverage

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

• 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

Investment in Stocks as a prportion of Wealth.

• Sell Stocks when the arise, buy stocks when they fall

It is the difference between Portfolio Value and NPV of the floor.

As long as the investor can tolerate the loss. We will adjust daily our portfolio.

1. Calculate NPV of Floor

2. Calculate the cushion

3. 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

We will sell, if they fall and we will buy, if the rise. It is a Convex strategy

Because the average investor holds the market portfolio

• The Market Portfolio itself is Buy and Hold

• demograpphic change

• porductivity

• government policies

1. During bad times, risk aversion could be very high

   • Equities perform bad

2. During good times, risk aversion is very low

   • Equities perform well

Because the behave same, the longrun investors has the advatage from the time horizon.

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

The Investor will change his portfolio every weight.

Yes, because equity covaries with consumption. If Consumption is low, returns of equity are low -> premium is needed to compesate the bearing risk

1. Eventhough there is a low conumption, with a reasonable risk aversion the risk premium should be below 1%.

2. The reasons are

   • Equity volatility is far higher thant consumption volatility

   • Equity returns are lowly correlated with consumption growth

The relative consumption and not the absolute consumption

A Investor take advatages from the long time horizon and use predictable returns to hedge against changes in the investment opportunity

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”.

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.

• For our understanding wether equities have high returns in the future

• Recommending an optimal asset allocation

They have a low correlation, sometimes even negative

X is the Asset weight

Wt+1 =

We should even invest in more stocks than the rebalancing demand

• Personal Risk

  • Liability-Hedging Portfolio

• Marekt Risk

  • Myopic Portfolio

• Aspirational Risl

  • Long Term Hedging Portfolio