Inter-temporal rate of substitution

Reading 55 - Economics and Investment Markets

Question about ITRS – the text says that an investor is willing to pay less (i.e. ITRS is relatively lower) for a bond during good economic times. Can someone explain why?

My intuition is that ITRS should be relatively higher, since the marginal utility of consumption today is lower during good times, and ITRS = Marginal utility of consumption in the future/ Marginal utility of consumption today.

Thoughts??

During good economic times, investors turn to stocks as they generate higher returns than bonds. Stock prices rise, bond prices fall.

Laissez les bons temps rouler!

Gotta separate the current state from the direction, and consumption from saving.

If you look only at the present, and times are bad, you will get a lot of pleasure from a little more. If you’re starving, buying a sandwich is massively satisfying. But if times are good and you buy your 6th umbrella – less “wow”. So, good times = low marginal utility of consumption now. Bad times = high marginal utility of consumption now.

If the economy is okay now, but you expect it will be terrible in the future, you’ll save for the rainy day by consuming less now – you’ll transfer “not consumption” to your future self. Your ITSR is thus high (because you’re like, “I will be starving next year so I should substitute consumption now on an intertemporal basis”). But if things are okay now and you expect them to be very good in the future – well, “Don’t Worry Be Happy!” Why save when you can drive Bentleys off piers, and live even larger in the golden age ahead. Your ITSL is very low (because you’re too coked out to pronounce “intertemporal”).

Now, buying a bond is not buying food. It’s the opposite. If you expect a dark age ahead, you want to transfer money to your future starving self (your ITSL is high) – you have to buy a bond and give up an extra sandwich. But if you expect a future in which unlimited robot butlers give free ass massages and no one wants for anything – well, sell all your bonds and buy a 12 million boxes of cinnamon toast crunch. And a Bentley.

I.e., during good economic times, and when you expect better economic times in the future, you spend more, save less, and thus are less keen on overpaying for a bond.

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Remember the mathematics!

ITRS = u1 / u0

Where u1 is the marginal utility of consuming in the future and u0 is the marginal utility of consuming today.

u0 is always higher than u1 except when economic enviroment is extremely bad (1929 for example, even 2008)

In good economic times or when good economic times are expected to come soon the marginal utility of consuming in the future gets lower because we prefer to consume today. So u1 decreases and u0 increases giving a new ITRS lower than before.

Also remember how the real risk-free rate is built from the IRTS:

Rf = (1 / IRTS) -1

Rf and IRTS are negatively related, so when IRTS decreases (good economic enviroment) the real risk-free rate gets higher. This plays exact with what TheMagician said: “in good economic times, investors prefer to invest in equity and less in bonds, bond prices get lower”. Lower bond prices give what? Yup, higher rates. Everything is chained.

Hope this helps.

Excellent explanation. Thanks to you and thanks to the magician also for his french sentence putting a pure light on a difficult concept to grasp for a simple french guy like me.

D’accord.

I assume this is for me (hope so).

Thanks for your gratitude, indeed. :grin:

You are welcome.

One quick question - why do we prefer to consume more now (u0) when times are good or expected to be better? Shouldn’t we prefer to consume less today and save for future (thus prefer higher u1)?

During good times, you have less need to save for the future. So you prefer current consumption (u0 higher, M lower). In bad times, you need to save more for the future. So you prefer future consumption (u1 higher, M higher).

I thought that during good times you would save for futures (potential) bad times, but that isn’t the case in this model?

“In “good” economic times, individuals may have relatively high levels of current income so that current consumption is high”.

Page 360, reading 50, bottom paragraph.

People do save for bad times, but when good economic times are present or coming, people start saving less for future subsistence and consuming more for current joy. It is logical and empirically proved.

If I do well in my job, I’m paid well, my boss trusts me, my colleagues say I’m always a good help, and the nation economy is growing consistently, then I will be more confident consuming more today, investing more today and probably _ saving a lesser proportion of my income _. Note the key word is “proportion”.

When I was a trainee some years ago, I saved not lower than 50% of my small income, because in case I decided to study full time, hate the job, or be fired, I would have positive resources to consume (u1 was practically equal to u0 for me, even considering the consumptions are in different times). By the time I got hired in a real job, my income went 4x. My saving rate dropped to 30% of my income.

Hope this helps.

Thank you so much for this explanation, pure gold!

There is still one thing that I struggle with. In the book (p380) they mention that (short version) “Good economic times cause high current consumption but the utility from each unit of consumption will be low”.

I interpret this as U0 will be lower, thus the IRTS will be higher (U1/U0), causing the risk free to be lower as the denominator in “1/IRTS - 1” is higher.

What at am I missing?

I think each new unit will result in a lower utility and accordingly U0 will always be higher than U1 to maintain the same rule of “Good times result in a lower ITSR”

Hope this helped!

It is talking about diminishing returns, which states that any additional unit consumed will provide a lower utility than the previous unit, so there comes a point when you stop consuming. It has total sense, I don’t know anybody that consumes 2 thousand cookies a month.

For the IRTS explanation, take what I wrote above and be safe for the exam :grin:

I still don’t get this.

In good times, you have high levels of current consumption so the marginal utility of current consumption is low. So the denominator is low, which means the ratio should be high, not low.

u0 should decrease, not increase.

We just have higher levels of current consumption. So much infact that the marginal utility shrinks as we consume more.