Ch1 & Ch8

[Rajat gupta]

Hello Everyone
I have two questions from Ch1 and Ch8. Please somebody help
What do we mean by "systematic forecast errors" in Shiller's proposition of Excessive Volatility?

What is difference between Markov Property and a Martingale?

Regards
Rajat

 

[John Potter]

Hi Rajat,

Can you please post questions on different topics as different posts? It's more helpful if people want to follow the trail of one of the questions.

Whilst a share price is theoretically the discounted value of all future dividends, we're not going to always get this right. However, Shiller's point was that whilst we might get it wrong (forecast error), we should not systematically get it wrong in the same way. This suggests we are systematically over-estimating or under-estimating the price.

Markov and Martingale are not really connected...

Markov means where go next depends at most on where we are now.
Any process with independent increments has the Markov property, eg Brownian motion.
Martingale means that we expect the future value to be the current value.

Standard Brownian motion has the Markov property and is a martingale.
General Brownian motion with drift has the Markov property and is NOT a martingale.
Let Xn = Xn-1 + Zn X0, where Zn ~ N(a,1)
This is NOT Markov because where we go next, Xn, depends not just on where we are now, Xn-1, but also on where we were in the past, X0.
If a=0, Xn is a martingale
If a <>0, Xn is not a martingale.

So, we have created a 2*2 grid here of Markov/NOT Markov versus Martingale/NOT Martingale.

Good luck!
John

 

[Rajat gupta]

Hi Rajat,

Can you please post questions on different topics as different posts? It's more helpful if people want to follow the trail of one of the questions.

Whilst a share price is theoretically the discounted value of all future dividends, we're not going to always get this right. However, Shiller's point was that whilst we might get it wrong (forecast error), we should not systematically get it wrong in the same way. This suggests we are systematically over-estimating or under-estimating the price.

Markov and Martingale are not really connected...

Markov means where go next depends at most on where we are now.
Any process with independent increments has the Markov property, eg Brownian motion.
Martingale means that we expect the future value to be the current value.

Standard Brownian motion has the Markov property and is a martingale.
General Brownian motion with drift has the Markov property and is NOT a martingale.
Let Xn = Xn-1 + Zn X0, where Zn ~ N(a,1)
This is NOT Markov because where we go next, Xn, depends not just on where we are now, Xn-1, but also on where we were in the past, X0.
If a=0, Xn is a martingale
If a <>0, Xn is not a martingale.

So, we have created a 2*2 grid here of Markov/NOT Markov versus Martingale/NOT Martingale.

Good luck!
John

Thanks a lot John for the great explanation!
How to post now questions of different topics as different post? Can I edit my original post. Please guide I would be happy to do so

 

[Rajat gupta]

Sir, What do we mean by "systematic" in my 1st question of Shiller's Proposition? Does it have any relationship with Specific or Systematic Risk we study in CAPM?

 

[John Potter]

Hi Rajat,

The only connection here is through the word "systematic" having a meaning in English, otherwise we're talking about 2 different topics really...

Systematic risk is the risk that is always there because a stock belongs to the market, always part of the same "system".
Systematic forecast errors are making forecast errors in the same way each time, always part of the same "system".

I don't think it's useful to connect these 2 concepts,

Good luck!
John

 

[Rajat gupta]

Hi Rajat,

The only connection here is through the word "systematic" having a meaning in English, otherwise we're talking about 2 different topics really...

Systematic risk is the risk that is always there because a stock belongs to the market, always part of the same "system".
Systematic forecast errors are making forecast errors in the same way each time, always part of the same "system".

I don't think it's useful to connect these 2 concepts,

Good luck!
John

Thanks Sir