acegolfer wrote: ↑Wed Nov 09, 2022 8:03 am
InvestInPasta wrote: ↑Wed Nov 09, 2022 6:29 am
So if I put $1000 in a 5 years bond with an YTM of 10%, how much money will I have at maturity date?

$1500? Is it correct?

yes, assuming it's a par bond with 10% coupon rate and you keep the coupons as cash (earning 0%). So the compounded annualized return (from terminal wealth after 5 yrs) would be (1500/1000)^(1/5) - 1 = 8.45% (less than 10% YTM).

Oicuryy wrote: ↑Tue Nov 08, 2022 5:31 pm
longvista wrote: ↑Tue Nov 08, 2022 12:17 pm
The critical point here is that the yield is not compounding - as @acegolfer puts it: It is a "non-compounded annualized return". However, CAGR

is a compounded annualized return.

As per the research paper, the original intention of the YTM metric is to talk about the "non-compounded annualized return" (yield), not CAGR. Somewhere along the way, people got confused and started interpreting YTM in the sense of CAGR, instead of yield. As @dbr puts it, they might be confusing return with yield.

YTM is a compounded rate of return. Here is how that research paper puts it. (emphasis in original)

Figure 1 shows how the present value amounts that sum to the bond’s $1,000 price are *earning* a 5% compound rate of return in becoming the coupon or face value that each represents, e.g., the $43.19 part of the $1,000 price has earned 5% compounded for 3 years when the $50 coupon is received in year 3 ($43.19 x 1.053). Since each dollar of the bond’s price is earning a 5% compound rate of return it follows that by paying the price of the bond and receiving the promised coupons and face value at maturity that the investor *earns* the calculated YTM.

https://www.economics-finance.org/jefe/ ... lpaper.pdf
Both CAGR and YTM are compounded rates. The difference is in how they treat the coupons. CAGR treats the coupons as if they were all paid on the maturity date. YTM treats the coupons as being paid on the dates they were actually paid.

Ron

When I see an expected return quoted somewhere for some kind of investment, my instinct is to calculate the total return that I would have after some time, if I invest in it. For example, if I see a 5%/year interest rate quoted for a $10,000 bank CD with a term of 3 years, I know that at the end of 3 years, I will have 3 * (5% * $10,000) + $10,000 = $11,500, so that's a total return of $1,500.

When I look at a bond on the market, I see its price, term, YTM and other details. My immediate instinct is to ask the same thing: if I invest in this, how big will my total return be? @InvestInPasta exemplifies this question well:

InvestInPasta wrote: ↑Wed Nov 09, 2022 6:29 am
So if I put $1000 in a 5 years bond with an YTM of 10%, how much money will I have at maturity date?

However, let's take a slightly different bond (where the price is different from the principal):

Code: Select all

```
Maturity: 5 years
Principal: $1,000
Current Price: $800
Coupon Payment: $50 / year
YTM: 10.32%
```

So how big is the total return at maturity, if I buy this bond? Yield To Maturity sounds like it would help me to calculate this. This seems to be confirmed by quotes like the following from Investopedia:

Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures.

The first instinct is to apply the same calculation methodology that I applied to the CD:

Code: Select all

```
5 * ($800 * 10.32%) = $412.8 (coupon payments)
$412.8 + ($1,000 - $800) = $612.8 (total return)
```

Hmm, didn't work. I should actually get:

I know that I can calculate the total return based on price, term, coupon amount and face value, but I want to calculate total return through YTM instead, because that's what I believe YTM should help me to find out.

I understand the definition of YTM, but I want to know its

uses. I know that YTM can be used to have an apples-to-apples comparison between different bonds, but I am interested in YTM for calculating total return for a coupon bond where the coupons are not reinvested.

**Question:** How can I use YTM in order to calculate my total return on a coupon bond (when coupons are not reinvested)? In which formula do I need to plug in the YTM?

**Question:** If calculating total return in this way is not possible, what is the intended, original use of YTM - is it only the apples-to-apples comparison?

**Question:** If calculating total return with YTM is not possible, then why does Investopedia think that YTM is related to total return - is it because of their erroneous interpretation of YTM as the CAGR in the case of coupon reinvestment?

**EDIT****: Fixed wrong YTM number, pointed out by acegolfer.**