Ch 7 Modelling Investment Returns

Question 1

Modelling Investment returns, variance and correlations

Comment on small changes in inputs (portfolio weights very sensitive to input parameters)

Answer 1

1. Portfolio weights are very sensitive to the input parameters … small changes in inputs can lead to large changes in outputs
2. Studies have shown that portfolio weights are about :
   11 x more sensitive to changes in forecast returns compared to volatility
   20x more sensitive to changes in forecast returns compared to correlation
3. In order of importance then, forecast returns, then forecast variance, then forecast correlation

Question 2

Modelling Investment returns, variance and correlations

Conservatism in modelling

Answer 2

1. Equal returns, volatility and zero correlation … equally weighted portfolio

Question 3

Conservatism in Modelling

Given correlation is the ‘least’ sensitive: equal returns, equal vol, small correlations (e.g. half of long term history) … will xxx portfolio vol due to xxx to risker assets

Answer 3

Given correlation is the ‘least’ sensitive: equal returns, equal vol, small correlations (e.g. half of long term history) … will UNDERESTIMATE portfolio vol due to an OVER ALLOCATION to risker assets

Question 4

Conservatism in Modelling

Unequal returns case 1 : constant risk/return multiple …

Answer 4

Unequal returns case 1 : constant risk/return multiple … a sensible approach if you do not have confidence in your ability to distinguish between assets

Question 5

Conservatism in Modelling

Unequal returns case 2 : if you believe long term history will repeat, ….

Answer 5

Unequal returns case 2 : if you believe long term history will repeat, then an application of shrinkage techniques to returns will assist

Question 6

Conservatism in Modelling

Unequal variances: equal returns, volatility set sensibly (e.g. judicious choice of history (should GFC be in?), applied to all similar assets (e.g. all equities, all govt bonds, etc.) ), small correlations … will xxxx assets with xxxx volatility …

Answer 6

Unequal variances: equal returns, volatility set sensibly (e.g. judicious choice of history (should GFC be in?), applied to all similar assets (e.g. all equities, all govt bonds, etc.) ), small correlations … will OVERWEIGHT assets with LOW volatility … they will be a better risk/return trade off

Question 7

How to squeeze extreme volatility and correlations towards the average

Answer 7

Use shrinkage and smoothing techniques (these help to minimise estimation errors

Question 8

Mean reversion is generally evident in: (3)

Break?

Answer 8

1. GDP Growth Rates
2. FX rates
3. Equities market

Can break - eg central bank intervention

Question 9

Mean reversion

Be aware of the LEVEL of key return drivers
- eg equities

Answer 9

For equity markets valuation is critical – markets that are very expensive or very cheap will change direction at some point, often sharply … beware of a bubble building

Question 10

Mean reversion - consider Momentum

Answer 10

1. greed & fear … trends can continue for much longer than is warranted by economic fundamentals
2. Consider serial correlation - there may be no justification for momentum but it could be worthwhikle factoring into models.

Question 11

Long Term Expectations

Fixed Income

Real GDP Growth = xxx + yyy

Answer 11

Real GDP Growth = Population growth + Productivity growth

Question 12

Long Term Expectations

Fixed Income
If Central Banks have neutral monetary policy and government budgets are balanced then

Answer 12

If Central Banks have neutral monetary policy and government budgets are balanced then

Short Term Risk Free Rate = Nominal GDP Growth
= Inflation + Real GDP Growth

Question 13

Long Term Expectations

Fixed Income
Long Term Risk Free Rate = ??
Note there is no insight, but the historic premium has been…

Answer 13

Long Term Risk Free Rate = Short Term Risk Free Rate + 0.5% to 1% pa

Question 14

Long term expectations - Fixed Income

Corporate Yield =

Answer 14

Corporate Yield = Risk Free Rate + Corporate Premium + Default Rate

Question 15

Long term expectations - Fixed Income
Corporate Premiums:
1. Range
2. Default rate

Answer 15

Corporate Premiums

1. have ranged between 70bps an 160bps in US, for A-grade bonds over government bonds. About 120bps seems reasonable
2. Default rate: about ~12bps over the last 25 years

Question 16

Long term expectations - Equities

1. Equity Price Return =
2. Equity Total Return = Nominal Growth Rate of Economy + Dividend Yield
3. Caveats
4. In practice

Answer 16

1. Equity Price Return = Nominal Growth Rate of Economy
2. Equity Total Return = Nominal Growth Rate of Economy + Dividend Yield
3. Caveats;
   a) The ERP has through most of history been implausibly large and implausibly volatile.
   b) Inflation shocks (usually positive) serve to return real bond returns and increase equity returns – equities are an inflation hedge
4. Practitioners assign a ‘base’ equity risk premium in the range of 3% - 7.5% and vary market returns based on valuation and other market risks

Question 17

Stein Estimates

• what are they
• what is the effect
• why are they important

Answer 17

What:
- Stein estimates involve moving a set of raw estimates towards their grand means.
Effect:
- This reduces the expected sum of the mean squared errors around the true means for a variety of distributions.
- Stein estimates reduce the sensitivity to estimation error in the individual parameters.
Importance:
- Thus reducing the sensitivity of the final mix to small changes in input parameters.