Embedded Value and PVFP

[cw812]

Hi all,

I am confused with the solution of September 2017 Question 5 (ii), which talks about switching from passive embedded value basis to market consistent embedded value basis. The solution talks about how PVFP might change when switching from a long-term rate to risk-free rate.

1. What is the long-term rate? I could not find its definition in the course notes.
2. How do we know that "it is expected that the risk-free rate is less than the current discount rate"? I understand that the lower the discount rate, the higher the PV of future cashflow assuming the amount is same.
3. How do we know that "the investment return used on corporate bonds would be lower under a risk-free approach compared to a passive approach"? And why does it "lower investment return lead to reduced PVFP"?

Thanks
cw812

 

[Sarah Byrne]

Hi cw812

It's worth starting by saying that many students struggled with this questions in the September 2017 exam - so don't panic if you are struggling understanding every point in the Examiners' Report. If you use ASET, you might find it helpful to look at the explanation of the solution given there. It also presents some points in a different way.

1. The long-term rate is the expected investment return that will achieved over the 'long-term'. Given we are told the mix of assets in the introduction, it is reasonable to assume that it is based on the expected long-term return on these assets.

2. The risk-free rate is generally set by considering the return on a government bond. As mentioned above, we are told the mix of assets held in the question, and it is reasonable to assume that the current discount rate (set based on the expected return on the assets held) would be higher than that expected on government bonds alone. So, the risk-free rate will be lower, leading to the higher value of the PVFP.

3. One of the requirements of a risk-free approach is that the investment return assumptions will all be at the risk-free rate, irrespective of the actual assets held. As mentioned above, investment return on a corporate bond would be expected to be higher than a government bond due to the additional liquidity and credit risk. So, changing to a risk-free approach (and using the government bond yield instead) will reduce the investment return. The PVFP is the discounted value of the future cashflows (premiums - benefits/claims - expenses + investment returns). If the investment return item falls it will therefore reduce the PVFP.

I hope this helps.

Kind regards
Sarah

 

[cw812]

Hi cw812

It's worth starting by saying that many students struggled with this questions in the September 2017 exam - so don't panic if you are struggling understanding every point in the Examiners' Report. If you use ASET, you might find it helpful to look at the explanation of the solution given there. It also presents some points in a different way.

1. The long-term rate is the expected investment return that will achieved over the 'long-term'. Given we are told the mix of assets in the introduction, it is reasonable to assume that it is based on the expected long-term return on these assets.

2. The risk-free rate is generally set by considering the return on a government bond. As mentioned above, we are told the mix of assets held in the question, and it is reasonable to assume that the current discount rate (set based on the expected return on the assets held) would be higher than that expected on government bonds alone. So, the risk-free rate will be lower, leading to the higher value of the PVFP.

3. One of the requirements of a risk-free approach is that the investment return assumptions will all be at the risk-free rate, irrespective of the actual assets held. As mentioned above, investment return on a corporate bond would be expected to be higher than a government bond due to the additional liquidity and credit risk. So, changing to a risk-free approach (and using the government bond yield instead) will reduce the investment return. The PVFP is the discounted value of the future cashflows (premiums - benefits/claims - expenses + investment returns). If the investment return item falls it will therefore reduce the PVFP.

I hope this helps.

Kind regards
Sarah

Thanks Sarah,

I think I have confused "long-term rate" and "current discount rate" at first. Your explanation is very clear. So the long term rate is the expected investment return, is it equivalent to 'yield' on the assets held? are they interchangeable?

 

[Mark Willder]

Thanks Sarah,

I think I have confused "long-term rate" and "current discount rate" at first. Your explanation is very clear. So the long term rate is the expected investment return, is it equivalent to 'yield' on the assets held? are they interchangeable?

Investment return and yield are not necessarily the same thing.

The yield on a bond is the interest rate that equates the present value of the cashflows to its price. So if we hold the bond to maturity the actual investment return we achieve will be equal to the initial gross redemption yield. However, if we sell the bond before maturity then the investment return will depend on the interest earned to date and any capital gain or loss on the sale.

The yield on shares is the current rate of dividend divided by the share price. This formula only looks at the income and ignores any capital gain. However the investment return will look at both income and capital gain.

Best wishes

Mark