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What is the yield to maturity of a fund comprised of fixed income securities?
What is the yield to maturity of a fund comprised of fixed income securities?

Understanding how we calculate yield for the Cash Plus fund

Written by Lovelyn
Updated over a week ago

The simple answer is that the yield to maturity of an investment is the interest rate earned when all expected interest payments are made and principal are repaid. It is then annualised to give a comparable figure for a year.

This can be applied to either a single investment or to a fund or portfolio as a weighted average. We think it is one of the most appropriate ways to explain the expected return (albeit subject to standard risks) of a fund comprised of fixed income securities such as the Kernel Cash Plus Fund, as it reflects what is currently in the portfolio, rather than what happened in the past.

After all, you don’t compare saving accounts or call deposit rates, based on what the published rate was 1 or 5 years ago.

To explain more thoroughly it’s probably easiest to consider some examples.

### Example one – a term deposit

If we invest \$100 and get \$104 back at the end of 1 year then this is a 4% yield to maturity – calculated as follows:

\$104 ÷ \$100 -1 = 0.04 = 4%

### Example two – a one year bond investment

Let’s consider investing in a bond with a notional value (or principal) of \$100 with one year to maturity that costs \$100 and pays 4% semi-annually.

This means that the bond will pay 2% after six months and a further 2% after one year.
In financial speak, this interest rate paid is called the coupon, but this is not the yield as we will see. The bond will also repay the notional value of \$100 at maturity.

The cash flows of the investment in the bond will be:

 Cashflow Note Today -\$100 investment of \$100 6 months +\$2 coupon of 4% ÷ 2 x \$100 12 months +\$102 \$100 principle + \$2 coupon (4% ÷ 2 x \$100)

In this case the yield to maturity is roughly the solution to this equation:

100 = 102 ÷ (1+ yield ) + 2 (1+yield)^0.5

The solution is yield = 4.04%.

How can this be? Shouldn’t the yield be the same as the coupon?
In this case the intuitive explanation is simple: this bond has a slightly better return characteristic to example one as we get \$2 six months earlier (and that \$2 could be reinvested for 6 months) so therefore the return must be a little bit better – which it is 4.04%, indeed a little higher than 4%!

### Example three – a one year bond investment in a discounted bond

Now let’s consider the same investment as in example two, but this time the \$100 notional bond now costs \$99. The market is valuing it a bit lower perhaps it’s perceived as a slightly risky investment, or perhaps the market is receiving higher yields from comparable alternatives. This time the cash flows will be:

 Cashflow Note Today -\$99 investment of \$99 – This is the only difference 6 months +\$2 4% ÷ 2 x \$100 12 months +\$102 \$100 principle + \$2 interest (4% ÷ 2 x \$100)

In this case the yield to maturity is roughly the solution to this equation:

99 = 102 ÷ (1+ yield ) + 2 (1+yield)^0.5

The solution is yield = 5.1%.

Intuitively we get 4% interest payments, but we save 1% at the beginning – so that’s roughly 5%, we also get half of the 4% early which means the yield will be higher than 5%. There are a few other reasons too, but that involves diving into the mathematics a bit more deeply.

### Example four – a two year mortgage

Suppose we take out a 2 year interest only mortgage for \$100,000 with a fixed interest rate of 6% p.a. paid in monthly installments and a 1% arrangement fee added to the principal then the cash flows would be as follows:

 Cashflow Principal Note Today \$100,000 \$101,000 1% fee added to principal Month 1 -\$505 \$101,000 =101,000 x 6% ÷ 12 Month 23 -\$505 \$101,000 =101,000 x 6% ÷ 12 Month 24 -\$101,505 \$101,000 Last interest payment + principal

In this case the yield to maturity is roughly the solution to this equation:

\$100,000 = \$101,000*6%/12 ÷ (1+yield) ^ (1/12) + …+ \$101,000*6%÷ 12 / (1+yield) ^ (23/12) + \$101,000*(1+6%÷ 12) / (1+yield)^(24÷ 12)

The solution is roughly 6.73%

Intuitively we can see there is a 1% fee that’s spread over two years – roughly 0.5% per year. Which takes the 6% rate to 6.5%. Then also as the interest rate is 6%, but its paid earlier than annually as its paid monthly throughout the year, so that makes the rate a bit higher and then we can get to the mathematical solution of 6.73% - which reflects the true cost of borrowing.

### Example five – a portfolio of investments

Now consider we have a portfolio of investments, being:

25% in a 1 year deposit at 4% (as in example one above), yield = 4%

75% in a one year discounted bond that costs \$99 (for \$100 principal) and pays a coupon of 4% (as in example three above), yield = 5.1%

The yield on the portfolio will be calculated as the weighted average of the yields of the underlying investments as follows:

0.25 * 0.04 + 0.75 * 0.051 = 0.04825 = 4.825%

Which makes intuitive sense – i.e the yield to maturity is somewhere between the two yields of the underlying investments.

### Summary

Yield to maturity and the coupon (or sometimes called interest) are two different things. Yield to maturity is the better measure of the expected future return on an investment as it factors in the timing of cash flows and gives a better measure of the rate that an investment will grow at. It is important to know when we speak of an interest rate whether it is the coupon or the yield – as you can see there can be a huge difference!

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