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As inflation is high, central banks such as the FED and the ECB hike rates.

One of the consequences is that the stock market is falling and in particular companies having a lot of debt (such as technologies companies, see NASDAQ vs Dow Jones).

States are also heavily indebted in the aftermath of the pandemic. What are the consequences of rising interest rates for governments? Does it make more difficult to borrow on markets? Will we see austerity policies for 'weak' countries within the EU?

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Heavily indebted states/Governments will see their cost of servicing (of the debt) rise when their central banks raise rates, future debt issuance will be costlier as well. If the debt in question is not inflation linked, then high inflation will compensate somehow (dept is good in inflationary times).

For now, the EU put in place an ‘anti-fragmentation’ tool, designed to prevent spreads between core and peripheral sovereign bonds from widening too far i.e ECB bond purchase program helping more indebted countries and preventing financial fragmentation within the currency bloc.

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It depends how quickly a company/ individual/ country rolls over their debt.

Imagine you have a mortgage that has an interest rate that is indexed to fed funds rate, you'll instantly feel the rate increase and you will instantly start trying to balance your books(austerity). Compared to if you have a 20 year fixed mortgage where you don't really care what the rate does. You have a lot of certainty with your cash flow.

Bonds are a bit different because you pay the interest then finish off the bond by paying back the principle amount and a lot of debt is 'rolled over' meaning you renew your debt and get the new interest rate. A lot of corporate debt is also indexed to LIBOR so rates are updated automatically.

To model this really well you'd want to look at the raw data and see when these roll overs/principle repayments are due and do some scenario analysis to get a fell for how this would look.

The big boys at investment banks/hedge funds already had this priced in before you were born so good luck trading on it!!!

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Not all stocks fall. Financials react well to rising rates.

When rates rise, that can be a sign for a booming economy, which means government will collect more tax/revenue. And if inflation is high, this means they'll pay less than they borrowed. So real-rates matter.

However, many governments (E.g. emerging markets) borrow in USD, and when USD rates rise their local currency suffers. So that might not be an easy circumstance.

So this is a multi facet situation.

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