Most significant factors in the price of a goverments bonds As a follow up on Long-,short-term interest rates and inflation.

Inflation is clearly a factor(tho not possible to model mathematically) when it comes to the market price of a bond. I can think of two ways in which it enters(in the short run), let me know weather these two are true or not i.e this is my main question,


Via the loss in value of nominal amount;this I extraced this from this quote


"Inflation is a bond's worst enemy. Inflation erodes the purchasing power of a bond's future cash flows. Put simply, the higher the current rate of inflation and the higher the (expected) future rates of inflation, the higher the yields will rise across the yield curve, as investors will demand this higher yield to compensate for inflation risk"[1]


Long term rates are the expected average of short term rates and the shortest i.e the funds rate is set to control inflation, the inflation expectations should be pretty much the same as short term rate expectations due to this, if this is how one should think about it. In conclusion, short term rate expectations and inflation expectations are pretty much the same thing and these in turn determine the longer term government bond rate.


Any comments on other factors and the logic behind their impact would be great to have

[1]https://www.investopedia.com/articles/bonds/09/bond-market-interest-rates.asp
1) The following quote is a poor description of how to look at bond markets.


  Inflation is a bond's worst enemy. Inflation erodes the purchasing
  power of a bond's future cash flows. Put simply, the higher the
  current rate of inflation and the higher the (expected) future rates
  of inflation, the higher the yields will rise across the yield curve,
  as investors will demand this higher yield to compensate for inflation
  risk"


The statement that higher expected inflation will raise nominal bond yields is outright incorrect. It assumes that real yields are constant. We can look at the inflation-linked market to see that real yields are highly variable, and in fact have moved more than inflation expectations in countries like Canada and the United States in the past couple of decades.

Trying to change that to assuming that inflation expectations rise and we assume that real yields are constant is just a way of saying that higher nominal yields generate capital losses for bonds. Everybody knows that already.

A proper analysis needs to look very carefully at what we mean by "inflation."


Is it observed inflation? Which measure - e.g., headline or core (ex-food and energy)?
Is it breakeven inflation, which can be extracted from inflation-linked bond prices?
Is it a survey of inflation expectations? However, we need a survey of bond investors, not economists or consumers - and such surveys are not available.


However, we can look at any of these definitions of inflation, and find cases where nominal bond yields fell, yet the inflation measure rose. For example, an oil price spike can be associated with a recession, which causes the central bank to cut interest rates.

As was pointed out in a comment, one could argue that poor inflation performance could raise term premia. (Essentially, adding an inflation risk premium on top of existing term premia.) This is a plausible argument. However, it is not exactly in line with the quoted text. It is not just “inflation” itself that is the problem - we already have inflation - rather, it has to be a significant burst of unanticipated inflation. However, most central banks would probably react violently to a big burst of inflation, and the curve would likely be fairly flat. Hard to distinguish between a term premium and rate expectations in that environment. In any event, that story is quite different than the quoted text from the external article.

2) The statement:


  the funds rate is set to control inflation, the inflation expectations
  should be pretty much the same as short term rate expectations due to
  this.


is incorrect. Once again, it assumes that the real rate is constant. This is certainly not the case. 

We can look at the Fed Funds rate (link to FRED database) and see that it has varied in a range from 0-5% since the early 2000s. Meanwhile, core PCE inflation (the Fed's preferred measure of inflation) has been stuck between 1-2.5% over that period. (link to FRED). Surveys of inflation have been similarly far more stable than nominal rates.

The only way to phrase this is to say that the central bank sets nominal interest rates at a level to keep inflation near target. Bond market pricing is heavily influenced by the expected path of those nominal rates -- although a term premium exists. However, if the inflation targeting is effective, there will be no link between observed inflation and nominal yields -- since real yields are being adjusted to keep inflation stable.

Take a look at the post-1995 history in Canada and the United States (and working from memory, the U.K., Australia, New Zealand...). Just plugging in "2%" (or sometimes 2.5%, depending on the inflation series) was a very effective "forecasting algorithm," and probably outperformed a lot of human forecasters. This did not mean that nominal yields were constant.